







The binomial theorem 
20100121 

Laura pose la question : Using the fact that (1 + x)^4 * (1 + x)^9 = (1 + x)^13 show (4C0 * 9C4 + 4C1*9C3 + 4C2*9C2 + 4C3*9C1 + 4C4*9C0) = 13C4 Harley Weston lui répond. 





nC0 + nC1 + nC2 + ... + nCn = 2^n 
20090615 

Chinonyerem pose la question : For n >= 1, derive the identity
nC0 + nC1 + nC2 + ... + nCn = 2^n
[Hint: Let a = b = 1 in the binomial theorem] Penny Nom lui répond. 





Square roots in a binomial expansion 
20060911 

Sydney pose la question : (√x + 5)^{4} expanded using the binomial theorem Penny Nom lui répond. 





What are the 3rd and 4th terms of (2xy)^7? 
20060618 

April pose la question : What are the 3rd and 4th terms of this sequence: (2xy)^{7}?
I'm having an issue with this...is there any easier way to get it without completely factoring the whoooole thing out? Penny Nom lui répond. 





Newton's binomial theorem 
20030830 

William pose la question : According to page 126 of Murtha & Willard's "Statistics and Calculus" (PrenticeHall, 1973), Newton's binomial theorem can proved inductively. I suppose that was his method, which I would like to see. Penny Nom lui répond. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

Tony pose la question : When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Andrei Volodin and Penny Nom lui répond. 





Multinomial theorem 
20011128 

Murray pose la question : Could you please state and explain the multinomial theorem (I already know the binomial theorem etc, to give you an idea of where i am) Harley Weston lui répond. 





The Binomial Theorem for rational exponents 
19990415 

Angela Evans pose la question : The full question is this: Isaac Newton generalized the Binomial Theorem to rational exponents. That is, he derived series of expansions for such expressions as (x+y)^{3} (x+y)^{2/3} (x+y)^{5/6} What did Newton find? What are the first four terms of the series expansions of binomials above? How can this extended Binomial Thrm. be used to aid in calculations? Penny Nom lui répond. 

