







Quel est le 6e nombre dans la serie suivante 
20100813 

jeff pose la question : Quel est le 6e nombre dans la serie suivante: 1,2,6,42,1806,... Stephen La Rocque and Claude Tardif lui répond. 





Une série géométrique 
20081123 

anass pose la question : je vx savoire est ce kil existe la somme de (1/n^x) avec n variant de 0 jusk à
infini
nota:
lorsk x=1et 2 la somme reste tjrs facile
mé lorsquil depasse 3 c difficile
et merci PierreLouis Gagnon lui répond. 





Loan payment formula 
20190224 

Kenneth pose la question :
I have a question regarding the loan payment formula shown below.
Calculating the Payment Amount per Period
The formula for calculating the payment amount is shown below.
Simple Amortization Calculation Formula
A = P X r(1 + r)n over (1 + r)n  1
where
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods
Is this formula/calculation a condensed version of a longer calculation? I am curious to know how the (1 +r)n  1 was developed from the longer calculation. For example, r(1 + r)n may have been (r + rn)n. The n's are exponents.
I thank you for whatever helpful explanation that may be provided.
Kenneth Harley Weston lui répond. 





A geometric series 
20180313 

nathi pose la question : Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres.
The maximum height part is not answered. Penny Nom lui répond. 





A road trip word problem 
20160410 

Marc pose la question : While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey? Penny Nom lui répond. 





Which term of the series 2+7+12+...is 152? 
20160201 

francis pose la question : whice term of the series 2+7+12+...is 152? Penny Nom lui répond. 





The sum of the first 50 terms of an arithmetic progression 
20140726 

Joshua pose la question : Hello ...my is Joshua...I'm a grade 11 student...I got a question
Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84 Penny Nom lui répond. 





An infinite geometric series 
20131224 

Muhammad pose la question : The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series Penny Nom lui répond. 





A sequence or a series? 
20130905 

Rahul pose la question : Whether the following sequence is increasing or decreasing? I even do not kow whether to call it a sequence or not. an = (1/(1+n))+(1/(2+n))+....+(1/(n+n)).
I am confused. It looks like a series to me. Please help.
Regards,
Rahul Robert Dawson lui répond. 





An arithmetic progression 
20120822 

A student pose la question : the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term. Penny Nom lui répond. 





1+2+4+8....= 1 
20120402 

Andy pose la question : In this minutephysics video, it's claimed that 1+2+4+8....= 1
Is this true, and if so, how?
< href="http://www.youtube.com/watch?v=kIq5CZlg8Rg">http://www.youtube.com/watch?v=kIq5CZlg8Rg Robert Dawson lui répond. 





A tree growth modelled by a geometric series 
20120208 

Steph pose la question : Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres Penny Nom lui répond. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

Vicki pose la question : I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Walter Whiteley lui répond. 





The sum of a series 
20111107 

Rattanjeet pose la question : Find the sum of 1(1/2) + 2(1/4) + 3(1/6) + 4(1/6)(3/4) + 5(1/6)(3/4)2 + 6(1/6)(3/4)3+ ... where 1/6 + (1/6)(3/4) + (1/6)(3/4)2 + ... constitutes a geometric series. Penny Nom lui répond. 





Infinite Logarithmic Series 
20110808 

Sourik pose la question : Dear Expert,
In my Amithabha Mitra and Shambhunath Ganguly's "A Text Book of Mathematics" I found the formula of log (1+x) where the base is e and x lies in between 1 and +1.As I want to learn Mathematics,I am not satisfied with the mere statement of the formula.Please help giving me the full proof.
Thanking you,
Sourik Robert Dawson lui répond. 





An imaginary infinite geometric tree 
20110218 

Elise pose la question : An imaginary infinite geometric tree grows 1m the first day.
2nd day 2 branches and right angles to each other and each 0.5 m long.
3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each.
And so on, infinitely.
Q: Use relationships of rightangled triangles and high school level knowledge of geometric series to show
the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m. Robert Dawson lui répond. 





A Taylor polynomial for (lnx)/x 
20100929 

Dave pose la question : I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, 3, 11, 50, 274... Ok, so the negative is an easy fix > (1)^n1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this?
Thanks! Chris Fisher lui répond. 





A geometric progression 
20100430 

Kalyani pose la question : sum of infinite geometric progression is 9 and common ratio is 1/10
then sum up to 8 terms is? Chris Fisher lui répond. 





1/1+1/2+1/3... 
20100331 

Mohd pose la question : you explained the way of getting the summation of 100 series numbers
but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100 Robert Dawson lui répond. 





A sequence of letters and numbers 
20091110 

Maria pose la question : What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old.
J1F8M1A0M1J0J1 Robert Dawson, Claude Tardif and Harley Weston lui répond. 





An infinite geometric series 
20090518 

terri pose la question : find the sum of the infinite geometric series
14 7 +7/2 7/4 +.....
A. 7007/13 B. 2002 C. 28/3 D.5005/7 Stephen La Rocque lui répond. 





2+6+12+20+30+42 
20090424 

fredy pose la question : what is the sigma notation for the series 2+6+12+20+30+42? Stephen La Rocque lui répond. 





The ratio test 
20090306 

Haley pose la question : Use the ratio test to determine whether the series in convergent or divergent.
(2/5)+(4/10)+(8/15)+... Harley Weston lui répond. 





Convergent or divergent? 
20090303 

Betsy pose la question : Use the ratio test to determine if the series is convergent or divergent.
1+1/2^2+1/3^3+1/4^4
I know the general terms are a(n)=1/n^n and a(n+1)=1/(n+1)^(n+1)
but I can't simplify r=lim(n>inf.)=n^n/(n+1)^(n+1) Robert Dawson lui répond. 





The middle term of an arithmetic sequence 
20081215 

Leigh pose la question : Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92 Penny Nom lui répond. 





An arithmetic series 
20081017 

Laura pose la question : In an arithmetic series 5+9+13+...+tn has a sum of 945. How many terms does the series have?
What formula do I use? Penny Nom lui répond. 





Demographics 
20080725 

shahrukh pose la question : Each year for 10 years ,the population of a city increased by 5% of its value in the previous year.
If the initial population was 200 000 ,what was the population after 10 years ?? Penny Nom lui répond. 





A series solution of y' = xy 
20080703 

sasha pose la question : I've to find the power series solution of the differential equation: y' = xy.
I don't know how to find the recursive equation. Can you please help me. Thanks Harley Weston lui répond. 





What number best completes the series? 
20071112 

Grace pose la question : What number best completes the series?
2 3 7 13 27 ____ Stephen La Rocque, Penny Nom and Harley Weston lui répond. 





Applications of sequences and series 
20070827 

Trish pose la question : I'm a grade 12 learner working on a math project based on sequences and series. I'd like to know the different types of sequences and series such as fibonacci, fourier, farey, etc.
I've already used the Fibonacci Sequence and Harmonic Series
and need two more.
The simpler the sequence or series type the better.
I'd also like to know in which nonmathematical areas use sequences and series
and how.
Areas such as engineering or science. Penny Nom lui répond. 





A sequence of circles 
20070611 

Ann pose la question : Please help with solving the following problem!!!
A circle is inscribed in an equilateral triangle with a side of length 2.
Three circles are drawn externally tangent to this circle and internally
tangent to 2 sides of the triangle. 3 more circles are drawn externally
tantgent to these circles and internally tangent to 2 sides of the triangle. if
this process continued forever, what would be the sum of the areas of all the
circle? the answer 1 parent came up with was Pie over 2, but we don't
know how he did it. Can you please show the work or explain the answer to
this problem?
Thank you
Ann
p s my daughter is in 9th grade math. Steve La Rocque, Chris Fisher and Penny Nom lui répond. 





A geometric series 
20070403 

jessica pose la question : If a geometric series includes 5418+62 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive. Stephen La Rocque lui répond. 





Arithmetic Series 
20070218 

Krista pose la question : Question The sum of the first 4 terms of an arithmetic series is 8 and the sum of the first 5 terms is 500. Determine the sum of the 3 terms. Stephen La Rocque lui répond. 





An arithmetic series 
20061128 

Jillian pose la question : Find the sum of 21 terms of an arithmetic series that has an eleventh term equal to 30. Penny Nom lui répond. 





Sigma from 0 to infinity of (n^3 / 3^n) 
20061115 

Cedric pose la question : I'm wondering how you would find if this series converges or diverges?
Sigma from 0 to infinity of (n^3 / 3^n)
Does the n^3 dominate, or does the 3^n dominate? What about higher powers like n^10 / 10 ^ n ? Which one would dominate then? Penny Nom lui répond. 





Adding consecutive numbers 
20060426 

Lisa pose la question : When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are?
Stephen La Rocque lui répond. 





Arithmetic Sums 
20060412 

Angel pose la question : (a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28.
(b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation. Stephen La Rocque lui répond. 





Sum of a Geometric Sequence 
20060411 

Andre pose la question : In a particular geometric sequence, U3=3.6 and U10=12.9. Find S16 and S17. Stephen La Rocque lui répond. 





Arithmetic progressions 
20060131 

A student pose la question : 1)the sum to n terms of a particular series is given by S_{n}=17n3n^{2}
a)find an expression for the n term of the series
b)show that the series is an arithmetic progression
2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference
Penny Nom lui répond. 





An Arithmetic sequence 
20051201 

Aana pose la question :
The first term in an arihmetic series is 25 and the 3rd term is 19. Find the number of terms in the series if its is 82.
Here's what I did to find d
a+2d=19; 25+2d= 19 ;1925=2d d=6/2=3
This is where I'm stuck. Can you please provide me with some guidance.
Penny Nom lui répond. 





The sum of a series 
20050831 

Aamod pose la question : Find the sum of the given series till n terms:
(1^{4}\1*3) + (2^{4}\3*5) + (3^{4}\5*7)............... till n terms Chri Fisher lui répond. 





The Maclaurin series generated by f(x)=x^ cosx + 1 
20050810 

Latto pose la question : f(x)=x^{3}·cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help?
Penny Nom lui répond. 





A geometric sequence 
20050621 

A student pose la question :
The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q. Penny Nom lui répond. 





A Taylor series for ln(x) 
20050416 

Anood pose la question : i have to represent ln(x) as a power series about 2
i`m not getting the final answer which is ln 2+ sigma (((1)^{(n+1)}/
(n*2^{n}))*(x2)^{n}). i don`t get the ln 2 part
i show you my trial
f(x)= ln x.
f(x)=(1/x) .
f(x)= (1/x^{2})*1/2!
f(x)= (2/x^{3})*1/3!
f(x)= (6/x^{4})* 1/4!
so the pattern shows me that f(n)= ((1)^{(n+1)})/x^{n} *n)
so f(2)= sigma ((1)^{(n+1)})/2^{n} *n) *(x2)^{n}
so as you see i don`t get ln 2
Penny Nom lui répond. 





Sum to n terms of the series i.(2^(ni)) 
20050128 

Satya pose la question : Sum to n terms of the series i.(2^{ni}) Penny Nom lui répond. 





The third derivative 
20041015 

Holly pose la question : Why would you ever take the third derivative? Harley Weston lui répond. 





The series from i=1 to n :ai 
20040818 

Ken pose la question : a.) Explain the difference between
the series from i=1 to n :ai
and the series j=1 to n :aj
b.) Explain the difference between
the series from i=1 to n:ai
and the series from i=1 to n :aj Penny Nom lui répond. 





Programming without trig functions 
20040525 

Derek pose la question : I am a programmer trying to calculate the following.
What is the formula to find the crosssectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?
I am using a PLC (programmable logic controller) to do this and trig functions are not available. Harley Weston lui répond. 





A geometric sequence 
20040413 

Michael pose la question : In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms. Penny Nom lui répond. 





Cosine of 35 degrees 
20040303 

Jason pose la question : How do you find the exact solution to cosine 35 degrees. Chris Fisher lui répond. 





A worm crawling home 
20040218 

Cindy pose la question : A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time? Penny Nom lui répond. 





A project about crosses 
20030610 

Joel pose la question :
I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)? Cross Number  Area sq cm  1  5  2  13  3  25  4  41  5  61  I also need to know what the formula is for it? Penny Nom lui répond. 





Chopping trees 
20030419 

Tamara pose la question :
The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him. He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work. Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down? Penny Nom lui répond. 





The sum of the first 1000 even integers 
20030206 

Jill pose la question : What is the sum of the first 1000 even integers? Paul Betts lui répond. 





Arithmitic sequence 
20030201 

A student pose la question : I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why. Claude Tardif lui répond. 





1+2+3+...+500 
20030131 

Brian pose la question : What is the sum of the numbers from 1 to 500 inclusive? Paul Betts lui répond. 





A bouncing ball 
20021214 

Eman pose la question :
Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.  Find the maximum height to which the ball rises after two bounces.
 Find the total distance that the ball has traveled when it hits the floor for the tenth time.
 Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.
Penny Nom lui répond. 





7+8+9+...+1000 
20020911 

Shirley pose la question : My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Penny Nom lui répond. 





My salary is doubled everyday for 30 days 
20020117 

Kanishk pose la question : I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?) Penny Nom lui répond. 





A geometric series 
20011024 

Tashalee pose la question : The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms? Penny Nom lui répond. 





Harmonic numbers 
20010523 

Leslie pose la question : The harmonic numbers H_{k}, k = 1,2,3.....are defined by H_{k} = 1 + 1/2 + 1/3....1/k I am trying to prove by mathematical induction: H_{2n} >= 1 + n/2 , whenever n is a nonnegative integer. H_{8} = H_{23} >= 1 + 3/2 Can you help? Harley Weston lui répond. 





A Taylor series 
20010427 

Karan pose la question : Given the following information of the function  f''(x) = 2f(x) for every value of x
 f(0) = 1
 f(0) = 0
what is the complete Taylor series for f(x) at a = 0 Harley Weston lui répond. 





Geometric and arithmetic sequences 
20010126 

Garry pose la question : what are the equations for geometric and arithmetic sequences? also, what are the equations for finding the sums of those series? Leeanne Boehm and Penny Nom lui répond. 





An infinite series 
20001216 

John pose la question : summation(n=1 to infinity)[n sin(1/(2n))]^{n} Harley Weston lui répond. 





Power series representations 
20001127 

Grace pose la question : Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1x), but beyond that I am lost. Harley Weston lui répond. 





Comparing an integral and a sum 
20001121 

Douglas Norberg pose la question : A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 2^{30} which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum. When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2^{x} from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Harley Weston lui répond. 





Infinite Geometric Series 
20001110 

Sam Carter pose la question : I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and r, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it. Harley Weston lui répond. 





Maclaurin series again 
20000923 

Jason Rasmussen pose la question : I suppose my confusion comes into play when I am trying to figure out where the x^{n} term comes from. I know that the Power Series notation is directly related to the Geometric Series of the form sigma [ br^{n} ] where the limit is b/(1r) for convergence at  r  <1. Therefore, the function f(x) needs to somehow take the form of b/(1(xa)), which may take some manipulation, and by setting r = (xa) and b = C_{n}, we get the Geometric Series converted to the Power Series. Taking the nth order derivative of the Power Series gives C_{n} = f^{n}(a)/n!. There must be a gap in my knowledge somewhere because I cannot seem to make f(x) = e^{x} take the form of f(x) = b/(1(xa)). Maybe I should have labelled my question as "middle" because it may be more of a personal problem with algebra and logarithms. Or, am I to assume that all functions can be represented by sigma [f^{n}(a) * (xa)^{n} / n!]? Harley Weston lui répond. 





A Maclaurin series 
20000921 

Jason Rasmussen pose la question : I have a question regarding power series notation for certain functions within the interval of convergence. Harley Weston lui répond. 





7     77 
20000913 

Peter pose la question : Does anyone know how to solve the following: 7 _ _ _ _ 77 ? I have to find the missing values. Chris Fisher and Walter Whiteley lui répond. 





1+4+9+16+...n^2 = n(n+1)(2n+1)/6 
20000601 

Shamus O'Toole pose la question : How do you derive that for the series 1+4+9+16+25.. that S(n)=(n(n+1)(2n+1))/6 Penny Nom lui répond. 





Geometric sequences 
20000411 

Jodie pose la question : I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much! Harley Weston lui répond. 





Approximations 
19991220 

Adrian Valc pose la question : Longtime ago I red an article about surprizing (and in a way frustrating) results in math, for example the limit of a nicely defined infinite series which was believed to be a simple rational number, but later was determined to be a transcendent number that missed the rational value by an incredibly small amount (so for example the limit proved to be 2.75000...00137.. with a lot of 0's in between). I cannot find that article anymore, so i was wondering if you have any such examples, or you can point to any relevant information source? Chris Fisher lui répond. 





Radius of convergence 
19990421 

Nowl Stave pose la question : Why is the radius of convergence of the first 6 terms of the power series expansion of x^(1/2) centered at 4 less than 6? Harley Weston lui répond. 





A Series 
19990420 

Deepak Shrestha pose la question : Given the sequence an=e^(n*Ln(n)), does the series converge and why? Harley Weston lui répond. 





Sequences and series 
19980527 

Michael Le Francois pose la question : The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term. The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term. Penny Nom lui répond. 

