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Solving Summation Expression

score 37 · Answer 1 · 2026-04-12 22:00:04

37

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Solving Summation Expression

Published on 12 Apr 2026 - 22:00

score 54 · Answer 2 · 2026-04-15 06:30:38

54

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Summation $\sum_{j=2}^{n-1}j^2$ Properties

Published on 15 Apr 2026 - 6:30

score 49 · Answer 3 · 2026-03-25 08:10:00

49

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Proof of a relation of Stickelberger element

Published on 25 Mar 2026 - 8:10

score 176 · Answer 4 · 2026-04-14 02:14:43

176

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About the closed form of $\sum _{k=1}^{n}\binom{n}{k}\frac{1}{k}$

Published on 14 Apr 2026 - 2:14

score 71 · Answer 5 · 2026-04-09 04:09:02

71

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How to prove the result of summing the divergent asymptotic sum for $H_n$?

Published on 09 Apr 2026 - 4:09

score 205 · Answer 6 · 2026-04-17 11:54:45

205

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Prove $\sum_{k=0}^{n}\binom{2k}{k}\binom{2(n-k)}{n-k}\frac{1}{(2k+1)(2n-2k+1)}=\frac{2^{\left(4n+1\right)}}{\left(n+1\right)^{2}\binom{2n+2}{n+1}}$

Published on 17 Apr 2026 - 11:54

score 478 · Answer 7 · 2026-04-08 18:14:05

478

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Summation rules for approaching a constant raises to the power of i?

Published on 08 Apr 2026 - 18:14

score 63 · Answer 8 · 2026-04-15 06:19:51

63

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Solution to some finite sum of reciprocals of odd integers (continuation)

Published on 15 Apr 2026 - 6:19

score 41 · Answer 9 · 2026-04-08 17:38:22

41

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Simplifying an equation with summation

Published on 08 Apr 2026 - 17:38

score 320 · Answer 10 · 2026-04-11 15:57:52

320

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How can you prove the Rothe–Hagen identity algebraically, not using Double Counting (combinatorics proof technique)?

Published on 11 Apr 2026 - 15:57

score 189 · Answer 11 · 2026-04-15 02:00:58

189

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3 binomial identities that I could not find a closed form for them

Published on 15 Apr 2026 - 2:00

score 123 · Answer 12 · 2026-03-25 19:09:58

123

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Given positives $a, b, c$ such that $a + b + c = 3$, prove that $\sum_{cyc}\frac{1}{a^2 + 4b^2 + c^2} \le \frac{1}{2}$.

Published on 25 Mar 2026 - 19:09

score 107 · Answer 13 · 2026-04-14 23:55:16

107

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What is the limit of the sum $\sum_{i=1}^{n}\frac{1}{b_i}$ for the decreasing sequence of positive integers $b_n=\frac{x+2^n-1}{2^n}$?

Published on 14 Apr 2026 - 23:55

score 266 · Answer 14 · 2026-04-09 18:13:00

266

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Somewhat challenging binomial identity

Published on 09 Apr 2026 - 18:13

score 97 · Answer 15 · 2026-04-11 12:10:25

97

Views

Closed form for $\sum_{k=0}^{n}\binom{\binom{n}{k}}{k}$

Published on 11 Apr 2026 - 12:10

List Question

Solving Summation Expression

Summation $\sum_{j=2}^{n-1}j^2$ Properties

Proof of a relation of Stickelberger element

About the closed form of $\sum _{k=1}^{n}\binom{n}{k}\frac{1}{k}$

How to prove the result of summing the divergent asymptotic sum for $H_n$?

Prove $\sum_{k=0}^{n}\binom{2k}{k}\binom{2(n-k)}{n-k}\frac{1}{(2k+1)(2n-2k+1)}=\frac{2^{\left(4n+1\right)}}{\left(n+1\right)^{2}\binom{2n+2}{n+1}}$

Summation rules for approaching a constant raises to the power of i?

Solution to some finite sum of reciprocals of odd integers (continuation)

Simplifying an equation with summation

How can you prove the Rothe–Hagen identity algebraically, not using Double Counting (combinatorics proof technique)?

3 binomial identities that I could not find a closed form for them

Given positives $a, b, c$ such that $a + b + c = 3$, prove that $\sum_{cyc}\frac{1}{a^2 + 4b^2 + c^2} \le \frac{1}{2}$.

What is the limit of the sum $\sum_{i=1}^{n}\frac{1}{b_i}$ for the decreasing sequence of positive integers $b_n=\frac{x+2^n-1}{2^n}$?

Somewhat challenging binomial identity

Closed form for $\sum_{k=0}^{n}\binom{\binom{n}{k}}{k}$

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