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Quandaries & Queries
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 Topic: binomial theorem
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 (2018^2019)-(2019^2018) 2019-01-23 From Nazrul:Find the remainder when (2018^2019)-(2019^2018) is divided by 4? Please show me the process.Answered by Harley Weston. A binomial expansion 2019-01-05 From shifali:if the binomial expansion of (m-nx)^3 is 1+9x+-- find the values of m & nAnswered by Penny Nom. The binomial theorem 2010-01-21 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) = 13C4Answered by Harley Weston. nC0 + nC1 + nC2 + ... + nCn = 2^n 2009-06-15 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 2006-09-11 From Sydney:(√x + 5)4 expanded using the binomial theoremAnswered by Penny Nom. What are the 3rd and 4th terms of (2x-y)^7? 2006-06-18 From April:What are the 3rd and 4th terms of this sequence: (2x-y)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 2003-08-30 From William:According to page 126 of Murtha & Willard's "Statistics and Calculus" (Prentice-Hall, 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 2002-01-20 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 2001-11-28 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 1999-04-15 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.

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