Question

How can I prove that $\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^{n}\exp(-\frac{(k-1)k}{2n})=0$?

score 147 · Answer 1 · 2026-04-14 13:06:06

147

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How can I prove that $\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^{n}\exp(-\frac{(k-1)k}{2n})=0$?

Published on 14 Apr 2026 - 13:06

score 77 · Answer 2 · 2026-04-15 10:15:46

77

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Sum of $\sum_{n=1}^k \frac{n}{(n+1)}$

Published on 15 Apr 2026 - 10:15

score 78 · Answer 3 · 2026-03-25 14:21:44

78

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How to analytically continue the ‘two-dimension’ zeta function?

Published on 25 Mar 2026 - 14:21

score 171 · Answer 4 · 2026-04-17 14:45:04

171

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Series prove using combinational argument

Published on 17 Apr 2026 - 14:45

score 71 · Answer 5 · 2026-04-17 14:18:11

71

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1•²⁵C₀ + 5•²⁵C₁ + 9•²⁵C₂ ..... 101•²⁵C₂₅ = 2²⁵ • k. Find the value of k.

Published on 17 Apr 2026 - 14:18

score 47 · Answer 6 · 2026-04-14 02:14:19

47

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Switching summation indices

Published on 14 Apr 2026 - 2:14

score 70 · Answer 7 · 2026-04-11 17:00:14

70

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Proof by Induction with summation and inequalities

Published on 11 Apr 2026 - 17:00

score 26 · Answer 8 · 2026-04-10 15:23:50

26

Views

Can't simplify this summation

Published on 10 Apr 2026 - 15:23

score 76 · Answer 9 · 2026-04-16 01:14:38

76

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Taylor Series inverse function

Published on 16 Apr 2026 - 1:14

score 107 · Answer 10 · 2026-04-14 02:20:27

107

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Explain how $\sum_{k = 1}^n\frac{k^2}{2^{k - 1}} = \sum_{k = 0}^{n - 1}\frac{\left(k + 1\right)^2}{2^k}$?

Published on 14 Apr 2026 - 2:20

score 1k · Answer 11 · 2026-04-16 07:37:32

1k

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Calculate sum of a row $\sum_{k=1}^{n}\left (2k-1\right )/2^k$

Published on 16 Apr 2026 - 7:37

score 63 · Answer 12 · 2026-04-15 19:28:25

63

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Does $\lim_{n \to \infty}\frac{n}{n + \sum_{k=1}^{n}k}$ converge to $0$ or $1$?

Published on 15 Apr 2026 - 19:28

score 161 · Answer 13 · 2026-04-08 21:27:25

161

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Value of $\sqrt{\sum_{k=1}^{1}k+\sqrt{\sum_{k=1}^{2}k+\sqrt{\sum_{k=1}^{3}k...}}}$

Published on 08 Apr 2026 - 21:27

score 37 · Answer 14 · 2026-04-11 16:47:32

37

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How to evaluate the closed form of the sum with factorials?

Published on 11 Apr 2026 - 16:47

score 83 · Answer 15 · 2026-04-10 17:53:07

83

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Alternating Series Error Approximation Not Working

Published on 10 Apr 2026 - 17:53

List Question

How can I prove that $\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^{n}\exp(-\frac{(k-1)k}{2n})=0$?

Sum of $\sum_{n=1}^k \frac{n}{(n+1)}$

How to analytically continue the ‘two-dimension’ zeta function?

Series prove using combinational argument

1•²⁵C₀ + 5•²⁵C₁ + 9•²⁵C₂ ..... 101•²⁵C₂₅ = 2²⁵ • k. Find the value of k.

Switching summation indices

Proof by Induction with summation and inequalities

Can't simplify this summation

Taylor Series inverse function

Explain how $\sum_{k = 1}^n\frac{k^2}{2^{k - 1}} = \sum_{k = 0}^{n - 1}\frac{\left(k + 1\right)^2}{2^k}$?

Calculate sum of a row $\sum_{k=1}^{n}\left (2k-1\right )/2^k$

Does $\lim_{n \to \infty}\frac{n}{n + \sum_{k=1}^{n}k}$ converge to $0$ or $1$?

Value of $\sqrt{\sum_{k=1}^{1}k+\sqrt{\sum_{k=1}^{2}k+\sqrt{\sum_{k=1}^{3}k...}}}$

How to evaluate the closed form of the sum with factorials?

Alternating Series Error Approximation Not Working

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