List questions from binomial-theorem

Published on 26 May 2021 - 3:29

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Reference and proof of binomial tail identity

Published on 26 May 2021 - 4:27

166

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DNA partition function

Published on 26 May 2021 - 16:44

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Problem on binomial coefficients

Published on 26 May 2021 - 17:42

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Finding closed form of $\sum\limits_{r=0}^n r^2 \binom nr p^{n-r}q^r$ where $p>0$ and $q=1-p$

Published on 28 May 2021 - 3:43

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How to simplify the Gamma functions such that the Binomial Theorem can be used?

Published on 28 May 2021 - 11:59

504

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$\sum_{r=0}^{100}{100\choose r}\sin(2rx)$ and $\sum_{r=0}^{100}{100\choose r}\cos(2rx)$

Published on 28 May 2021 - 12:37

104

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Binomial theorem and sum from $k = 0$ to $N/2$

Published on 29 May 2021 - 17:50

170

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Inverse Laplace transform of $\frac{a\sinh\left[\frac{p}{c}(L-x)\right]}{p\sinh\left[\frac{pL}{c}\right]}$ with respect to $p$ using binomial theorem

Published on 30 May 2021 - 21:09

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Proof for Binomial Expression

Published on 31 May 2021 - 8:23

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Inequality of binomial coefficients

Published on 31 May 2021 - 10:24

126

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Q is to prove that integer just above ($\sqrt{3} + 1)^{2n}$ is divisible by $2^{n+1}$ for all n belongs to natural numbers.

Published on 01 Jun 2021 - 12:22

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$^nC_r$ summation series

Published on 05 Jun 2021 - 7:22

360

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Closed form expression of $ \sum_{k=0}^n (3k^3 +2k^2 -3k +2) r^k {n \choose k} $

Published on 06 Jun 2021 - 17:37

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Finding $n>2$ such that $a_1$, $a_2$, $a_3$ are in arithmetico-geometric progression and $\left(1-x^3\right)^n=\sum_{r=0}^na_rx^r(1-x)^{3n-2r}$

Published on 07 Jun 2021 - 15:26

List Question

Coefficient of $x^n$ in logarithmic series

Reference and proof of binomial tail identity

DNA partition function

Problem on binomial coefficients

Finding closed form of $\sum\limits_{r=0}^n r^2 \binom nr p^{n-r}q^r$ where $p>0$ and $q=1-p$

How to simplify the Gamma functions such that the Binomial Theorem can be used?

$\sum_{r=0}^{100}{100\choose r}\sin(2rx)$ and $\sum_{r=0}^{100}{100\choose r}\cos(2rx)$

Binomial theorem and sum from $k = 0$ to $N/2$

Inverse Laplace transform of $\frac{a\sinh\left[\frac{p}{c}(L-x)\right]}{p\sinh\left[\frac{pL}{c}\right]}$ with respect to $p$ using binomial theorem

Proof for Binomial Expression

Inequality of binomial coefficients

Q is to prove that integer just above ($\sqrt{3} + 1)^{2n}$ is divisible by $2^{n+1}$ for all n belongs to natural numbers.

$^nC_r$ summation series

Closed form expression of $ \sum_{k=0}^n (3k^3 +2k^2 -3k +2) r^k {n \choose k} $

Finding $n>2$ such that $a_1$, $a_2$, $a_3$ are in arithmetico-geometric progression and $\left(1-x^3\right)^n=\sum_{r=0}^na_rx^r(1-x)^{3n-2r}$

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