List questions from summation

Published on 12 Apr 2026 - 4:40

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Finding the sum of a sequence of terms

Published on 11 Apr 2026 - 7:33

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Sum of products of binomial coefficients: $ \sum_{l=0}^{n-j} \binom{M-1+l}{l} \binom{n-M-l}{n-j-l} = \binom{n}{j} $

Published on 17 Apr 2026 - 5:42

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Summation of infinite series

Published on 13 Apr 2026 - 17:07

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Proving $\sum_{k=0}^n\dfrac{x_k^{n+1}}{\prod_{j\neq k}(x_k-x_j)}=\sum_{k=0}^nx_k$

Published on 16 Apr 2026 - 9:15

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Sum of a Sequnce

Published on 12 Apr 2026 - 8:14

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What does this infinite sum converge to?: $\sum_{n=1}^\infty \frac1{n^k} = \frac1{1^k} + \frac1{2^k} + \frac1{3^k} + ...$

Published on 14 Apr 2026 - 8:10

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Summation of series- substitution

Published on 14 Apr 2026 - 15:09

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Help finding a summation using CAS

Published on 10 Apr 2026 - 22:05

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Help in explaining this sigma notation breakdown

Published on 11 Apr 2026 - 15:04

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Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$

Published on 17 Apr 2026 - 7:45

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What's $\sum_{k=0}^n\binom{n}{2k}$?

Published on 11 Apr 2026 - 23:09

551

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Divisor function asymptotics

Published on 10 Apr 2026 - 21:27

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Solving the Riemann Sum $\sum_{i=1}^{n}(1+\frac{6i}{n})^3(\frac{2}{n})$?

Published on 13 Apr 2026 - 21:13

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Integral $\int^1_0\frac{\ln{x} \ \mathrm{Li}_2(x)}{1-x}dx$

Published on 17 Apr 2026 - 14:14

List Question

Interesting combinatorial identities

Finding the sum of a sequence of terms

Sum of products of binomial coefficients: $ \sum_{l=0}^{n-j} \binom{M-1+l}{l} \binom{n-M-l}{n-j-l} = \binom{n}{j} $

Summation of infinite series

Proving $\sum_{k=0}^n\dfrac{x_k^{n+1}}{\prod_{j\neq k}(x_k-x_j)}=\sum_{k=0}^nx_k$

Sum of a Sequnce

What does this infinite sum converge to?: $\sum_{n=1}^\infty \frac1{n^k} = \frac1{1^k} + \frac1{2^k} + \frac1{3^k} + ...$

Summation of series- substitution

Help finding a summation using CAS

Help in explaining this sigma notation breakdown

Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$

What's $\sum_{k=0}^n\binom{n}{2k}$?

Divisor function asymptotics

Solving the Riemann Sum $\sum_{i=1}^{n}(1+\frac{6i}{n})^3(\frac{2}{n})$?

Integral $\int^1_0\frac{\ln{x} \ \mathrm{Li}_2(x)}{1-x}dx$

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