List questions from summation

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Prove the inequality between integral and summation of multiplicative inverse

Published on 17 Apr 2026 - 10:20

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How to simplify a sum involving the floor function

Published on 09 Apr 2026 - 12:50

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Proving $\sum_{k=0}^n \binom n k (-2)^n =(-1)^n$

Published on 15 Apr 2026 - 6:46

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Evaluating the sums $\sum\limits_{n=1}^\infty\frac{1}{n \binom{kn}{n}}$ with $k$ a positive integer

Published on 11 Apr 2026 - 20:24

51

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Sum of Logarithms of expoenetial functions

Published on 11 May 2026 - 3:13

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Evaluating a limit involving summation

Published on 10 Apr 2026 - 21:36

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Concern about infinite sums

Published on 13 Apr 2026 - 18:34

309

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Finding a closed form solution

Published on 11 Apr 2026 - 9:32

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Prove inequality $(a_1+a_2+...+a_n)(\frac1{a_1}+\frac1{a_2}+...+\frac1{a_n})\geq n^2$ when $a_1,a_2,...,a_n$ are positive numbers.

Published on 16 Apr 2026 - 7:29

95

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Symmetry in Analytic Continuation of $\sum_{n=0}^{\infty} e^{-x E_n}$

Published on 25 Mar 2026 - 22:03

108

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Calculate $\sum_{n=1}^\infty \dfrac{nx}{e \ ^ {nx}}$

Published on 14 Apr 2026 - 12:12

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Sum identity using Stirling numbers of the second kind

Published on 12 Apr 2026 - 6:23

192

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What's the shortest way to prove $\sum_{t=1}^n t^2=\frac{n(n+1)(2n+1)}6$ by a mathematical induction?

Published on 16 Apr 2026 - 9:18

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A formula for $\int\limits_0^\infty (\frac{x}{e^x-1})^n dx$

Published on 15 Apr 2026 - 12:52

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The pigeonhole principle - how to solve questions like that?

Prove the inequality between integral and summation of multiplicative inverse

How to simplify a sum involving the floor function

Proving $\sum_{k=0}^n \binom n k (-2)^n =(-1)^n$

Evaluating the sums $\sum\limits_{n=1}^\infty\frac{1}{n \binom{kn}{n}}$ with $k$ a positive integer

Sum of Logarithms of expoenetial functions

Evaluating a limit involving summation

Concern about infinite sums

Finding a closed form solution

Prove inequality $(a_1+a_2+...+a_n)(\frac1{a_1}+\frac1{a_2}+...+\frac1{a_n})\geq n^2$ when $a_1,a_2,...,a_n$ are positive numbers.

Symmetry in Analytic Continuation of $\sum_{n=0}^{\infty} e^{-x E_n}$

Calculate $\sum_{n=1}^\infty \dfrac{nx}{e \ ^ {nx}}$

Sum identity using Stirling numbers of the second kind

What's the shortest way to prove $\sum_{t=1}^n t^2=\frac{n(n+1)(2n+1)}6$ by a mathematical induction?

A formula for $\int\limits_0^\infty (\frac{x}{e^x-1})^n dx$

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