List questions from binomial-theorem

Published on 17 Aug 2020 - 23:33

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Deriving expectation and variance for Binomial random variable

Published on 04 Apr 2026 - 1:05

204

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summation over partial multinomial coefficients

Published on 27 Mar 2026 - 7:11

49

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Why is $(n+1)^3 = \sum_{k=0}^n (k+1)^3 - k^3$?

Published on 26 Mar 2026 - 8:14

70

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Who can list more strings from given alphabets?

Published on 27 Mar 2026 - 5:55

127

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Finding $\sum_{k=0}^{n} (-1)^k \frac{k}{n \choose k}$, when $n$ is a positive integer

Published on 21 Aug 2020 - 8:04

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A question involving the expansion of $(x+2)^n$

Published on 21 Aug 2020 - 8:26

404

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Proving that $ \sum_{k=0}^\infty\frac1{2k+1}{2k \choose k}^{-1}=\frac {2\pi}{3\sqrt{3}} $

Published on 22 Aug 2020 - 6:36

140

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Proving a sum of a strange series $ \sum_{i=1}^{n} 11i^{10}-55i^9+165i^8-330i^7+462i^6 -462i^5+330i^4-165i^3+55i^2-11i+1 = n^{11} $

Published on 26 Mar 2026 - 9:50

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Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan

Published on 25 Mar 2026 - 6:13

115

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Integrating to derive relation between binomial co-efficient

Published on 24 Aug 2020 - 21:36

47

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Determining the sign of this binomial expression as function of its parameters

Published on 30 Mar 2026 - 0:19

40

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Proving binomial sum (checking my answer)

Published on 28 Aug 2020 - 18:48

1k

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count of subsets with sum divisible by $3$

Published on 02 Apr 2026 - 17:06

113

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Can we prove that $2^{-x}\sum_{k=0}^{\infty} {x \choose k} =1, x \in R^+$

Published on 01 Sep 2020 - 12:26

List Question

Coefficient of $x^7y^6$ in $(xy+x+3y+3)^8$

Deriving expectation and variance for Binomial random variable

summation over partial multinomial coefficients

Why is $(n+1)^3 = \sum_{k=0}^n (k+1)^3 - k^3$?

Who can list more strings from given alphabets?

Finding $\sum_{k=0}^{n} (-1)^k \frac{k}{n \choose k}$, when $n$ is a positive integer

A question involving the expansion of $(x+2)^n$

Proving that $ \sum_{k=0}^\infty\frac1{2k+1}{2k \choose k}^{-1}=\frac {2\pi}{3\sqrt{3}} $

Proving a sum of a strange series $ \sum_{i=1}^{n} 11i^{10}-55i^9+165i^8-330i^7+462i^6 -462i^5+330i^4-165i^3+55i^2-11i+1 = n^{11} $

Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan

Integrating to derive relation between binomial co-efficient

Determining the sign of this binomial expression as function of its parameters

Proving binomial sum (checking my answer)

count of subsets with sum divisible by $3$

Can we prove that $2^{-x}\sum_{k=0}^{\infty} {x \choose k} =1, x \in R^+$

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