Question

Express the following sum in terms of $n$: $\sum_{k=1}^{n} ( \frac{1}{2k-1}-\frac{1}{2k+1})$

score 183 · Answer 1 · 2026-04-13 11:45:15

183

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Express the following sum in terms of $n$: $\sum_{k=1}^{n} ( \frac{1}{2k-1}-\frac{1}{2k+1})$

Published on 13 Apr 2026 - 11:45

score 214 · Answer 2 · 2026-04-29 20:16:44

214

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Bounds on Egyptian fractions

Published on 29 Apr 2026 - 20:16

score 37 · Answer 3 · 2026-04-14 01:09:24

37

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Identity of sum $\sum_{a}^{b}x=-\sum_{b}^{a}x$

Published on 14 Apr 2026 - 1:09

score 392 · Answer 4 · 2026-04-14 05:08:56

392

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Sum over integers

Published on 14 Apr 2026 - 5:08

score 142 · Answer 5 · 2026-04-12 12:56:41

142

Views

Closed form for two binomial identities

Published on 12 Apr 2026 - 12:56

score 114 · Answer 6 · 2026-04-12 02:40:18

114

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Problem with two binomial identities from Concrete mathematics book

Published on 12 Apr 2026 - 2:40

score 92 · Answer 7 · 2026-04-12 04:40:51

92

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What is $\sum_{k=1}^n{{n}\choose{k}}k^{3}$ equal to?

Published on 12 Apr 2026 - 4:40

score 523 · Answer 8 · 2026-04-15 13:09:31

523

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How to compute $\lim\limits_{n\to\infty}\frac{1}{\sqrt{4n^2-1^2}}+\dots+\frac{1}{\sqrt{4n^2-n^2}}$.

Published on 15 Apr 2026 - 13:09

score 101 · Answer 9 · 2026-04-12 19:54:59

101

Views

"Simple" Summation Identity involving Gamma Functions

Published on 12 Apr 2026 - 19:54

score 165 · Answer 10 · 2026-04-15 19:05:28

165

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Closed form for $\sum_{k=1}^{n}\binom{n}{k}\frac{\left(-1\right)^k }{k}$ and $\sum_{k=1}^{n}\binom{n}{k}\frac{1 }{k+m}$

Published on 15 Apr 2026 - 19:05

score 116 · Answer 11 · 2026-04-11 20:16:12

116

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A closed form for $\sum_{k=0}^n \frac{(-1)^k {n \choose k}^2}{(k+1)^2}$

Published on 11 Apr 2026 - 20:16

score 29 · Answer 12 · 2026-04-12 20:47:17

$\sum \limits_{k~ \in~ K_e} \frac{a^k}{k!} - \sum \limits_{k~ \in~ K_o} \frac{a^k}{k!} = \sum \limits_{k=0}^{\infty} \frac{(-a)^k}{k!}$

score 97 · Answer 13 · 2026-04-13 21:32:02

97

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Truncated sum of $e^x$

Published on 13 Apr 2026 - 21:32

score 57 · Answer 14 · 2026-04-11 13:39:05

57

Views

Summation of Binomial Expansion with multiplicative factors

Published on 11 Apr 2026 - 13:39

score 60 · Answer 15 · 2026-04-17 10:11:08

60

Views

Closed form of $\sum_{k=0}^{m}\binom{k}{n}\left(-1\right)^k$

Published on 17 Apr 2026 - 10:11

List Question

Express the following sum in terms of $n$: $\sum_{k=1}^{n} ( \frac{1}{2k-1}-\frac{1}{2k+1})$

Bounds on Egyptian fractions

Identity of sum $\sum_{a}^{b}x=-\sum_{b}^{a}x$

Sum over integers

Closed form for two binomial identities

Problem with two binomial identities from Concrete mathematics book

What is $\sum_{k=1}^n{{n}\choose{k}}k^{3}$ equal to?

How to compute $\lim\limits_{n\to\infty}\frac{1}{\sqrt{4n^2-1^2}}+\dots+\frac{1}{\sqrt{4n^2-n^2}}$.

"Simple" Summation Identity involving Gamma Functions

Closed form for $\sum_{k=1}^{n}\binom{n}{k}\frac{\left(-1\right)^k }{k}$ and $\sum_{k=1}^{n}\binom{n}{k}\frac{1 }{k+m}$

A closed form for $\sum_{k=0}^n \frac{(-1)^k {n \choose k}^2}{(k+1)^2}$

$\sum \limits_{k~ \in~ K_e} \frac{a^k}{k!} - \sum \limits_{k~ \in~ K_o} \frac{a^k}{k!} = \sum \limits_{k=0}^{\infty} \frac{(-a)^k}{k!}$

Truncated sum of $e^x$

Summation of Binomial Expansion with multiplicative factors

Closed form of $\sum_{k=0}^{m}\binom{k}{n}\left(-1\right)^k$

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