List questions from binomial-theorem

169

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Prove for that $(1 + \frac{x}{p})^p < (1 + \frac{x}{q})^q$ [without Bernoulli inequality or integrals]

Published on 20 Apr 2016 - 11:45

90

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Intuitive proof for a Combinatorial Problem

Published on 21 Apr 2016 - 6:41

833

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Show that a power series is analytic inside its radius of convergence

Published on 21 Apr 2016 - 12:10

1.6k

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Catalan numbers formula derivation

Published on 29 Mar 2026 - 4:49

1k

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Generating function for multiset formula

Published on 26 Mar 2026 - 14:26

5.8k

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Intuitive explanation of extended binomial coefficient

Published on 24 Apr 2016 - 14:09

101

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Expand $f(x)=\log(x+ \sqrt{1+x^2})$ into power series and determine convergence intervals

Published on 24 Apr 2016 - 16:23

98

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Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$

Published on 25 Apr 2016 - 17:17

2.1k

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Binomial expansion extension to negative powers

Published on 28 Apr 2016 - 8:40

3.7k

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binomial coefficient where k > n

Published on 29 Apr 2016 - 1:56

105

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Simple Question on Binomial theorems...

Published on 29 Apr 2016 - 11:32

72

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Tricky divergent binomial expansions?

Published on 02 Apr 2026 - 7:09

118

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Finding lim${_{n \rightarrow \infty}}\left( \frac{n^3}{2^n} \right)$

Published on 05 May 2016 - 18:30

83

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Under what conditions can I split a power of a binomial sum into two products?

Published on 06 May 2016 - 12:17

90

Views

Determine the coefficient of $x^{18}$ in $\left(x+\frac{1}{x}\right)^{50}$

Published on 06 May 2016 - 19:39

List Question

Prove for that $(1 + \frac{x}{p})^p < (1 + \frac{x}{q})^q$ [without Bernoulli inequality or integrals]

Intuitive proof for a Combinatorial Problem

Show that a power series is analytic inside its radius of convergence

Catalan numbers formula derivation

Generating function for multiset formula

Intuitive explanation of extended binomial coefficient

Expand $f(x)=\log(x+ \sqrt{1+x^2})$ into power series and determine convergence intervals

Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$

Binomial expansion extension to negative powers

binomial coefficient where k > n

Simple Question on Binomial theorems...

Tricky divergent binomial expansions?

Finding lim${_{n \rightarrow \infty}}\left( \frac{n^3}{2^n} \right)$

Under what conditions can I split a power of a binomial sum into two products?

Determine the coefficient of $x^{18}$ in $\left(x+\frac{1}{x}\right)^{50}$

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