List questions from binomial-theorem

Published on 17 Sep 2017 - 11:56

43

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Prove $(1+p)^{p^{n-2}} = 1+p^{n-1}+up^n$ for some $u$

Published on 18 Sep 2017 - 5:34

66

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What is the co-efficient of $x^2$ in the expansion of $(x+\frac{1}{x^2})^{20}$?

Published on 21 Sep 2017 - 13:24

63

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Show that order of $p+1$ in $\mathbb{Z}_{p^n}$ is $p^{n-1}$.

Published on 21 Sep 2017 - 18:34

108

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$ \left( 1 - \frac{x}{n}\right)^n \leq \left( 1 - \frac{x}{n+1}\right)^{n+1} $, $\forall$ $x$ $\in$ $[0,n]$

Published on 31 Mar 2026 - 7:21

202

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Binomial Theorem and $n(n+1)2^{n-2} = \sum_{i=1}^ni^2\binom{n}{i}$

Published on 22 Sep 2017 - 4:14

141

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How can I prove that $2^n\ge n^4$?

Published on 26 Sep 2017 - 23:28

54

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Simplifying algebraic sum with binomial coefficients

Published on 30 Sep 2017 - 23:05

72

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Prove: $x^2<2^x$, $\forall x\ge x_0$, $x\in \Bbb R$

Published on 01 Oct 2017 - 12:06

267

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Is there a combinatorial "proof" for this special case of the multinomial theorem?

Published on 26 Mar 2026 - 4:32

97

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Question on the controversial "undefined" $0^0$

Published on 27 Mar 2026 - 12:08

597

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Prove that $3^n > 3n$ for integer $n\geq2$

Published on 28 Mar 2026 - 20:05

201

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Why can't we differentiate $x^x$ like we differentiate $x^3$ (e.g.)?

Published on 08 Oct 2017 - 18:52

347

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Single summation form

Published on 09 Oct 2017 - 14:49

6.5k

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The number of terms in the Multinomial Expansion $(x+\frac{1}{x}+x^2+\frac{1}{x^2})^n$

Published on 26 Mar 2026 - 4:35

List Question

How large is the term $abz$ in $(a+b+z)^n$ as $n$ approaches 2 in Binomial Theorem

Prove $(1+p)^{p^{n-2}} = 1+p^{n-1}+up^n$ for some $u$

What is the co-efficient of $x^2$ in the expansion of $(x+\frac{1}{x^2})^{20}$?

Show that order of $p+1$ in $\mathbb{Z}_{p^n}$ is $p^{n-1}$.

$ \left( 1 - \frac{x}{n}\right)^n \leq \left( 1 - \frac{x}{n+1}\right)^{n+1} $, $\forall$ $x$ $\in$ $[0,n]$

Binomial Theorem and $n(n+1)2^{n-2} = \sum_{i=1}^ni^2\binom{n}{i}$

How can I prove that $2^n\ge n^4$?

Simplifying algebraic sum with binomial coefficients

Prove: $x^2<2^x$, $\forall x\ge x_0$, $x\in \Bbb R$

Is there a combinatorial "proof" for this special case of the multinomial theorem?

Question on the controversial "undefined" $0^0$

Prove that $3^n > 3n$ for integer $n\geq2$

Why can't we differentiate $x^x$ like we differentiate $x^3$ (e.g.)?

Single summation form

The number of terms in the Multinomial Expansion $(x+\frac{1}{x}+x^2+\frac{1}{x^2})^n$

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