List questions from binomial-theorem

Published on 14 Oct 2020 - 21:45

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Binomial theorem real world use

Published on 15 Oct 2020 - 4:45

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Let $f_{n}(x) = \dfrac{1}{n!}x^n(1-x)^n. $ Prove that the t-th derivative of the function evaluated at $0$ is an integer.

Published on 15 Oct 2020 - 11:02

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Finding Coefficients Terms

Published on 15 Oct 2020 - 16:53

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Computation of the sum involving product of binomial coefficients

Published on 30 Mar 2026 - 3:56

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In the ring $\mathbb{Z}_p$, $p$ is prime, $(a+b)^p=a^p+b^p$ proof?

Published on 05 Apr 2026 - 13:48

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Proof of orthogonality of binomial coefficients

Published on 16 Oct 2020 - 9:55

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Why can we not expand $(a+b)^n$ directly when $n$ is a fractional or negative index?

Published on 16 Oct 2020 - 10:49

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How to prove $1+(n+1)x \le (1+x)^{n+1}$?

Published on 16 Oct 2020 - 12:51

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Sums of power of positive integers via binomial theorem

Published on 17 Oct 2020 - 14:07

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Prove the inequality $(1-a)^b>(1-b)^a$ if $1>b>a>0$ by using binomial expansion

Published on 17 Oct 2020 - 19:21

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Summation of Binomial Coefficients with geometric series

Published on 19 Oct 2020 - 21:17

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Negative multinomial expansion

Published on 23 Feb 2026 - 23:57

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How do you solve this binomial proof?

Published on 30 Mar 2026 - 5:31

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Proof that $\sin x=4^{-x/\pi}\sum_{n=0}^\infty (-1)^n\binom{4x/\pi}{2n+1}$ for $x\ge 0$

Published on 29 Oct 2020 - 12:40

List Question

Proving that $\sum_{k=0}^{k=n} \binom{2n}{k} \cdot k = 2^{2n -1} \cdot n$

Binomial theorem real world use

Let $f_{n}(x) = \dfrac{1}{n!}x^n(1-x)^n. $ Prove that the t-th derivative of the function evaluated at $0$ is an integer.

Finding Coefficients Terms

Computation of the sum involving product of binomial coefficients

In the ring $\mathbb{Z}_p$, $p$ is prime, $(a+b)^p=a^p+b^p$ proof?

Proof of orthogonality of binomial coefficients

Why can we not expand $(a+b)^n$ directly when $n$ is a fractional or negative index?

How to prove $1+(n+1)x \le (1+x)^{n+1}$?

Sums of power of positive integers via binomial theorem

Prove the inequality $(1-a)^b>(1-b)^a$ if $1>b>a>0$ by using binomial expansion

Summation of Binomial Coefficients with geometric series

Negative multinomial expansion

How do you solve this binomial proof?

Proof that $\sin x=4^{-x/\pi}\sum_{n=0}^\infty (-1)^n\binom{4x/\pi}{2n+1}$ for $x\ge 0$

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