







The binomial theorem 
20100121 

From Laura: 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 Answered by Harley Weston. 





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

From Chinonyerem: For n >= 1, derive the identity
nC0 + nC1 + nC2 + ... + nCn = 2^n
[Hint: Let a = b = 1 in the binomial theorem] Answered by Penny Nom. 





Square roots in a binomial expansion 
20060911 

From Sydney: (√x + 5)^{4} expanded using the binomial theorem Answered by Penny Nom. 





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

From April: 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? Answered by Penny Nom. 





Newton's binomial theorem 
20030830 

From William: 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. Answered by Penny Nom. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom. 





Multinomial theorem 
20011128 

From Murray: 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) Answered by Harley Weston. 





The Binomial Theorem for rational exponents 
19990415 

From Angela Evans: 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? Answered by Penny Nom. 

