List questions from binomial-theorem

Published on 25 Jun 2018 - 20:04

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The relationship between the Pascal's triangle/sequence and the binomial number theorem?

Published on 28 Jun 2018 - 7:15

62

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Is it possible to extract a variable out of a bounded sum of binomial coefficients

Published on 29 Jun 2018 - 11:04

452

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Multinomial theorem & combinatorial probabilities

Published on 25 Mar 2026 - 7:38

37

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A curve C has an equation of $y = f(x)$, where $ f(x) = \frac{4x}{\sqrt{4+x}+\sqrt{4-x}} $, and $ -4\le x\le4. $

Published on 02 Jul 2018 - 17:22

930

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Remainder on division with $22$

Published on 25 Mar 2026 - 23:51

71

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Problem using binominal theorem?

Published on 25 Mar 2026 - 14:18

42

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Evaluating the variance of the biinomial distribution directly

Published on 04 Jul 2018 - 6:13

107

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Question wrt Binomial theorem

Published on 08 Jul 2018 - 8:48

689

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Derivation of Binomial theorem

Published on 10 Jul 2018 - 12:42

69

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Simplify and compute the MGF of $[1-(1-(1-e^{-ax})^{N_1})(1-(1-e^{-ax})^{N_2})]^{M-1} $

Published on 25 Mar 2026 - 14:34

123

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Coefficient of $x^k$ in ${(1 - e^x)}^{-n}$

Published on 11 Jul 2018 - 5:42

76

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How to simplify $\sum _{l=1} ^{k} \sum_{j_1 \ge 1} \cdots \sum_{j_l \ge 1, j_1 + \cdots + j_l=k} \binom{k}{j_1 \cdots j_l} \binom{-2}{l} 2^l$

Published on 25 Mar 2026 - 14:35

479

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Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

Published on 15 Jul 2018 - 20:45

1.8k

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Why binomial expansion approximation works?

Published on 18 Jul 2018 - 10:16

List Question

What is the range of convergence of $\sum_{n=0}^{\infty} {(-1)}^n\binom{1/2}{n}\frac{1}{2n+3}.$

The relationship between the Pascal's triangle/sequence and the binomial number theorem?

Is it possible to extract a variable out of a bounded sum of binomial coefficients

Multinomial theorem & combinatorial probabilities

A curve C has an equation of $y = f(x)$, where $ f(x) = \frac{4x}{\sqrt{4+x}+\sqrt{4-x}} $, and $ -4\le x\le4. $

Remainder on division with $22$

Problem using binominal theorem?

Evaluating the variance of the biinomial distribution directly

Question wrt Binomial theorem

Derivation of Binomial theorem

Simplify and compute the MGF of $[1-(1-(1-e^{-ax})^{N_1})(1-(1-e^{-ax})^{N_2})]^{M-1} $

Coefficient of $x^k$ in ${(1 - e^x)}^{-n}$

How to simplify $\sum _{l=1} ^{k} \sum_{j_1 \ge 1} \cdots \sum_{j_l \ge 1, j_1 + \cdots + j_l=k} \binom{k}{j_1 \cdots j_l} \binom{-2}{l} 2^l$

Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

Why binomial expansion approximation works?

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