Question

How to calculate this sum: $\sum_{k=1}^{n} \frac{k}{n^k} \binom nk$

score 198 · Answer 1 · 2026-04-11 18:36:12

198

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How to calculate this sum: $\sum_{k=1}^{n} \frac{k}{n^k} \binom nk$

Published on 11 Apr 2026 - 18:36

score 99 · Answer 2 · 2026-04-11 02:57:48

99

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Calculate sum with binomial coefficients: $\sum_{k=0}^{n} \frac{1}{k+1} \binom nk x^{k+1}$

Published on 11 Apr 2026 - 2:57

score 135 · Answer 3 · 2014-03-27 11:53:40

135

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$\sum (-1)^{n+1} n^{1/n} $ is not converging?

Published on 27 Mar 2014 - 11:53

score 94 · Answer 4 · 2026-04-11 11:03:04

94

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Can this double sum be simplified?

Published on 11 Apr 2026 - 11:03

score 149 · Answer 5 · 2026-04-09 04:48:00

149

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Simple proof explanation - Possibly triangle inequality involved

Published on 09 Apr 2026 - 4:48

score 1k · Answer 6 · 2026-04-03 01:05:46

1k

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How prove this sum $\sum_{n=1}^{\infty}\binom{2n}{n}\frac{(-1)^{n-1}H_{n+1}}{4^n(n+1)}$

Published on 03 Apr 2026 - 1:05

score 823 · Answer 7 · 2026-04-11 17:21:19

823

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Determining value of infinite sum after computing full Fourier Series

Published on 11 Apr 2026 - 17:21

score 175 · Answer 8 · 2026-04-02 18:18:55

175

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Can't find an identity for proving that $ \sum_{k=0}^{i+1} \binom {i+1} k=2^{i+1}$

Published on 02 Apr 2026 - 18:18

score 44 · Answer 9 · 2014-03-30 08:43:30

44

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Sum of combinations with a condition

Published on 30 Mar 2014 - 8:43

score 46 · Answer 10 · 2026-03-27 12:08:23

46

Views

Is there an expression for $(S/k)$ where $S=\sum_{n=1}^\infty n$ and $k \in \mathbb{Z}$?

Published on 27 Mar 2026 - 12:08

score 251 · Answer 11 · 2014-03-30 12:35:20

251

Views

Find highest $m$ such that $\sum\limits_{n=0}^m 9(n+1)10^n\le10^i$ for very large $i$

Published on 30 Mar 2014 - 12:35

score 132 · Answer 12 · 2026-04-03 01:01:33

132

Views

One Binomial Equation $\sum_{i=0}^{z} {n_1 \choose i}{n_2 \choose z-i} = {n_1+n_2 \choose z}$

Published on 03 Apr 2026 - 1:01

score 157 · Answer 13 · 2014-03-30 14:30:17

157

Views

Show $\lim_{x \to0^+} \sum_{n=1}^{\infty} \frac{2x}{n^2x^2+1} = \pi$

Published on 30 Mar 2014 - 14:30

score 70 · Answer 14 · 2026-04-08 23:19:47

70

Views

How to find this sum

Published on 08 Apr 2026 - 23:19

score 107 · Answer 15 · 2026-04-09 18:08:13

107

Views

How to get this sum

Published on 09 Apr 2026 - 18:08

List Question

How to calculate this sum: $\sum_{k=1}^{n} \frac{k}{n^k} \binom nk$

Calculate sum with binomial coefficients: $\sum_{k=0}^{n} \frac{1}{k+1} \binom nk x^{k+1}$

$\sum (-1)^{n+1} n^{1/n} $ is not converging?

Can this double sum be simplified?

Simple proof explanation - Possibly triangle inequality involved

How prove this sum $\sum_{n=1}^{\infty}\binom{2n}{n}\frac{(-1)^{n-1}H_{n+1}}{4^n(n+1)}$

Determining value of infinite sum after computing full Fourier Series

Can't find an identity for proving that $ \sum_{k=0}^{i+1} \binom {i+1} k=2^{i+1}$

Sum of combinations with a condition

Is there an expression for $(S/k)$ where $S=\sum_{n=1}^\infty n$ and $k \in \mathbb{Z}$?

Find highest $m$ such that $\sum\limits_{n=0}^m 9(n+1)10^n\le10^i$ for very large $i$

One Binomial Equation $\sum_{i=0}^{z} {n_1 \choose i}{n_2 \choose z-i} = {n_1+n_2 \choose z}$

Show $\lim_{x \to0^+} \sum_{n=1}^{\infty} \frac{2x}{n^2x^2+1} = \pi$

How to find this sum

How to get this sum

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