List questions from summation

Published on 13 Apr 2026 - 18:16

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Is there any way to calculate the following sum:$G(n)=\sum_{i=0}^ni\cdot f(i)$?

Published on 16 Apr 2026 - 2:50

42

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Finding whole number solution to a multi variable nonlinear equation

Published on 11 Apr 2026 - 1:31

146

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A $p$-congruence involving binomial coefficients and the floor function.

Published on 15 Apr 2026 - 17:56

106

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Set up a summation notation from a sequence

Published on 27 Mar 2026 - 5:54

105

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Sum of product of binomial coefficients.

Published on 14 Apr 2026 - 9:12

121

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Evaluate $f(n,j)=\sum _{k=0}^n k^{2 j} (-1)^{n-k} \binom{2 n}{n-k}$

Published on 17 Apr 2026 - 4:33

57

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Prove the following expression with induction

Published on 13 Apr 2026 - 17:01

204

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Is there any closed form for $\sum_{k=0}^{n}k^{r}\binom{n}{k}$?

Published on 13 Apr 2026 - 7:18

75

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Conjecture on the solutions to the equation $J(x) = J(x+a)$

Published on 13 Apr 2026 - 5:29

87

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Unbounded series with finite Cesàro mean

Published on 09 Apr 2026 - 12:01

83

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Formula of a polynomial with n roots

Published on 26 Mar 2026 - 14:25

135

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Is $\sum_{n=1}^{\infty} \frac{1}{\operatorname{lcm}[1,~2,~\ldots,~n]}$ irrational?

Published on 13 Apr 2026 - 21:34

297

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Verify that $4r^3+r=\left(r+\frac{1}{2}\right)^4-\left(r-\frac{1}{2}\right)^4$

Published on 17 Apr 2026 - 10:41

197

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sum of binomial series with alternate terms

Published on 14 Apr 2026 - 2:11

List Question

Find expression for following summation

Is there any way to calculate the following sum:$G(n)=\sum_{i=0}^ni\cdot f(i)$?

Finding whole number solution to a multi variable nonlinear equation

A $p$-congruence involving binomial coefficients and the floor function.

Set up a summation notation from a sequence

Sum of product of binomial coefficients.

Evaluate $f(n,j)=\sum _{k=0}^n k^{2 j} (-1)^{n-k} \binom{2 n}{n-k}$

Prove the following expression with induction

Is there any closed form for $\sum_{k=0}^{n}k^{r}\binom{n}{k}$?

Conjecture on the solutions to the equation $J(x) = J(x+a)$

Unbounded series with finite Cesàro mean

Formula of a polynomial with n roots

Is $\sum_{n=1}^{\infty} \frac{1}{\operatorname{lcm}[1,~2,~\ldots,~n]}$ irrational?

Verify that $4r^3+r=\left(r+\frac{1}{2}\right)^4-\left(r-\frac{1}{2}\right)^4$

sum of binomial series with alternate terms

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