List questions from binomial-theorem

Published on 30 Mar 2026 - 23:19

107

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Prove that $a^{p^2}\equiv a^p\pmod{p^2}$ for every $a\in\mathbb{Z}$

Published on 21 May 2015 - 16:15

265

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Show that the following expansion is valid for first $n$ terms

Published on 29 Mar 2026 - 2:17

415

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Show that the binomial series satisfies: $(1+x)f'(x)=\alpha f(x)$

Published on 22 May 2015 - 15:58

2.7k

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Find the remainder when $(x+1)^n$ is divided by $(x-1)^3$

Published on 23 May 2015 - 8:31

859

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Odd Power terms of binomial theorem proof

Published on 26 May 2015 - 10:58

127

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Show that the expansion of $(1+x)^n$ by Binomial Theorem is convergent when $x<1$

Published on 28 May 2015 - 6:23

450

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Falling power of a sum in terms of falling powers of the terms

Published on 26 Mar 2026 - 8:23

763

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Binomial expansion with negative power?

Published on 30 May 2015 - 21:48

56

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Solving equation with many exponents for same variable

Published on 31 May 2015 - 11:48

39

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Why can the function $f(x)=||A\vec{x}-\vec{b}||^2$ be rewritten as $\vec{x}^tA^tA\vec{x}−\vec{x}^tA^t\vec{b}−\vec{b}^tA\vec{x}+||\vec{b}||^2$

Published on 01 Jun 2015 - 20:47

221

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binomial expression of a powered term

Published on 03 Jun 2015 - 16:20

207

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Convergence of a binomial expansion

Published on 06 Jun 2015 - 14:17

470

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Can you show me a good approach for taking the limit of this function?

Published on 06 Jun 2015 - 17:43

443

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Simplifying the binomial expansion

Published on 06 Jun 2015 - 21:33

List Question

Lower bounding the binomial summation

Prove that $a^{p^2}\equiv a^p\pmod{p^2}$ for every $a\in\mathbb{Z}$

Show that the following expansion is valid for first $n$ terms

Show that the binomial series satisfies: $(1+x)f'(x)=\alpha f(x)$

Find the remainder when $(x+1)^n$ is divided by $(x-1)^3$

Odd Power terms of binomial theorem proof

Show that the expansion of $(1+x)^n$ by Binomial Theorem is convergent when $x<1$

Falling power of a sum in terms of falling powers of the terms

Binomial expansion with negative power?

Solving equation with many exponents for same variable

Why can the function $f(x)=||A\vec{x}-\vec{b}||^2$ be rewritten as $\vec{x}^tA^tA\vec{x}−\vec{x}^tA^t\vec{b}−\vec{b}^tA\vec{x}+||\vec{b}||^2$

binomial expression of a powered term

Convergence of a binomial expansion

Can you show me a good approach for taking the limit of this function?

Simplifying the binomial expansion

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