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 Sujet: converge
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 Convergent or divergent? 2009-03-03 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. Sigma from 0 to infinity of (n^3 / 3^n) 2006-11-15 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. A sequence that converges to e 2003-03-16 Dane pose la question :Something I noticed fooling around with a calculator about 30 years ago. Considering e = 2.718281828459045.... Using Window's Calculator you will find 1.111 = 2.8531167... 1.01101 = 2.731861... 1.0011001 = 2.71964085... 1.000110001 = 2.71841774... 1.00001100001 = 2.7182954... 1.00000110000011 = 2.178231875... 1.000000110000001 = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'11'infinite number of zeros'1 = e. Penny Nom lui répond. Harmonic numbers 2003-03-12 Becky pose la question :What can you tell me about the limit of harmonic numbers as it reaches infinity?Penny Nom lui répond. Power series representations 2000-11-27 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/(1-x), but beyond that I am lost. Harley Weston lui répond. Radius of convergence 1999-04-21 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 1999-04-20 Deepak Shrestha pose la question :Given the sequence an=e^(-n*Ln(n)), does the series converge and why?Harley Weston lui répond. Neighbourhoods 1996-02-14 Robert pose la question :What are neighbourhoods?Harley Weston lui répond.

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