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How to solve $\sum_{k=1}^{\infty} ke^{-k}$?

score 2.7k · Answer 1 · 2026-03-25 06:10:34

2.7k

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How to solve $\sum_{k=1}^{\infty} ke^{-k}$?

Published on 25 Mar 2026 - 6:10

score 93 · Answer 2 · 2026-03-25 14:22:28

93

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summing terms to the cardinality all possible subsets of a given set

Published on 25 Mar 2026 - 14:22

score 176 · Answer 3 · 2026-03-26 05:18:02

176

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A sum of sum involving binomial coefficent.(my conjecture)

Published on 26 Mar 2026 - 5:18

score 297 · Answer 4 · 2026-03-25 19:30:44

297

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Prove that $ \frac{\sin(2m+1) \theta}{\sin \theta} = 1 + 2 \cos2\theta + 2\cos4\theta+\dots+2 \cos2m\theta$

Published on 25 Mar 2026 - 19:30

score 155 · Answer 5 · 2026-03-25 11:20:49

155

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Is there another prime $p$ such that $S(p)$ is prime?

Published on 25 Mar 2026 - 11:20

score 196 · Answer 6 · 2026-03-25 04:42:54

196

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How to prove $e^x\ge \left(1+\frac xn\right)^n$ for any real numbers $x, n > 0$

Published on 25 Mar 2026 - 4:42

score 2.6k · Answer 7 · 2018-02-27 05:53:34

2.6k

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Third Moment of Geometric Series?

Published on 27 Feb 2018 - 5:53

score 979 · Answer 8 · 2018-02-27 07:49:03

979

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Why is it that $\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$ is not less than $\int_1^\infty \frac{dx}{x^2} = 1$?

Published on 27 Feb 2018 - 7:49

score 60 · Answer 9 · 2026-03-25 03:21:27

60

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$ \sum_{t=0}^{N}\left ( \frac{B(t) -C(t)}{(1+Z)^t} \right )=0 $, Solve for $Z$

Published on 25 Mar 2026 - 3:21

score 125 · Answer 10 · 2018-02-27 20:01:51

125

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Geometric Summations that reference two variables

Published on 27 Feb 2018 - 20:01

score 145 · Answer 11 · 2018-02-27 21:19:28

145

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how to rewrite this equation to solve for P?

Published on 27 Feb 2018 - 21:19

score 126 · Answer 12 · 2018-02-27 22:47:52

126

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Summation involving binomial coefficient, exponent and another term

Published on 27 Feb 2018 - 22:47

score 96 · Answer 13 · 2018-02-28 03:49:58

96

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Proving recurrence $S_{k+1}(n) = \sum_{i=1}^n i^{k+1}$

Published on 28 Feb 2018 - 3:49

score 145 · Answer 14 · 2026-03-25 13:57:54

145

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Let $(a_n)_{n=1}^\infty$ be an infinite sequence of complex numbers. Prove the following limit.

Published on 25 Mar 2026 - 13:57

score 559 · Answer 15 · 2026-03-25 06:21:38

559

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The most peculiar totient sum: $\sum_{n=1}^{\infty} \frac{\phi(n)}{5^n +1}$

Published on 25 Mar 2026 - 6:21

List Question

How to solve $\sum_{k=1}^{\infty} ke^{-k}$?

summing terms to the cardinality all possible subsets of a given set

A sum of sum involving binomial coefficent.(my conjecture)

Prove that $ \frac{\sin(2m+1) \theta}{\sin \theta} = 1 + 2 \cos2\theta + 2\cos4\theta+\dots+2 \cos2m\theta$

Is there another prime $p$ such that $S(p)$ is prime?

How to prove $e^x\ge \left(1+\frac xn\right)^n$ for any real numbers $x, n > 0$

Third Moment of Geometric Series?

Why is it that $\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$ is not less than $\int_1^\infty \frac{dx}{x^2} = 1$?

$ \sum_{t=0}^{N}\left ( \frac{B(t) -C(t)}{(1+Z)^t} \right )=0 $, Solve for $Z$

Geometric Summations that reference two variables

how to rewrite this equation to solve for P?

Summation involving binomial coefficient, exponent and another term

Proving recurrence $S_{k+1}(n) = \sum_{i=1}^n i^{k+1}$

Let $(a_n)_{n=1}^\infty$ be an infinite sequence of complex numbers. Prove the following limit.

The most peculiar totient sum: $\sum_{n=1}^{\infty} \frac{\phi(n)}{5^n +1}$

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