Question

Compute $\sum_{x\in\mathcal{N}}\sum_{y\in\mathcal{N}}\frac{1}{x+y+1}$

score 137 · Answer 1 · 2026-04-16 23:13:25

137

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Compute $\sum_{x\in\mathcal{N}}\sum_{y\in\mathcal{N}}\frac{1}{x+y+1}$

Published on 16 Apr 2026 - 23:13

score 116 · Answer 2 · 2026-04-14 05:08:30

116

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Sum of reciprocals of perimeters of primitive Pythagorean triples

Published on 14 Apr 2026 - 5:08

score 79 · Answer 3 · 2026-04-12 23:07:38

79

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Show that $\frac{1}{x^x}$ is continuous on $[0,1]$, and find its integral on this range.

Published on 12 Apr 2026 - 23:07

score 1k · Answer 4 · 2026-04-17 07:47:34

1k

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Proving $\pi=(27S-36)/(8\sqrt{3})$, where $S=\sum_{n=0}^\infty\frac{\left(\left\lfloor\frac{n}{2}\right\rfloor!\right)^2}{n!}$

Published on 17 Apr 2026 - 7:47

score 78 · Answer 5 · 2026-04-15 15:32:14

78

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A summation involving the inverses of the products of the elements of subsets of a set

Published on 15 Apr 2026 - 15:32

score 113 · Answer 6 · 2026-04-08 19:15:25

113

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Finding an identity to simplify this combinatorics solution

Published on 08 Apr 2026 - 19:15

score 44 · Answer 7 · 2026-04-16 07:01:03

44

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$\sum_i \frac{1}{x^{1/2^i}}$

Published on 16 Apr 2026 - 7:01

score 94 · Answer 8 · 2026-04-15 13:31:04

94

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Solution to $\sum_{0\leq n_1\leq n_2\leq\cdots\leq n_\beta\leq\gamma}{(-1)^{n_1+n_2+\cdots+n_\beta}}$

Published on 15 Apr 2026 - 13:31

score 206 · Answer 9 · 2026-04-10 01:16:35

206

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Sum $\sum_{k=1}^n{k(k-1)}$

Published on 10 Apr 2026 - 1:16

score 67 · Answer 10 · 2026-04-15 13:15:28

67

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How to show $\sum_{i=0}^{2m} (-1)^{i}\binom{2m}{i}^{2} = (-1)^m\binom{2m}{m}$

Published on 15 Apr 2026 - 13:15

score 179 · Answer 11 · 2026-04-13 05:13:10

179

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Using integral comparison to estimate how fast the partial sums of $\sum_{k=1}^N\frac1{k^3}$ converge

Published on 13 Apr 2026 - 5:13

score 156 · Answer 12 · 2026-04-17 13:30:50

156

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A strange inequality

Published on 17 Apr 2026 - 13:30

score 26 · Answer 13 · 2026-04-16 15:19:49

26

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Question about $x \in \text{Img}(X)$

Published on 16 Apr 2026 - 15:19

score 53 · Answer 14 · 2026-03-25 12:50:53

53

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How do I prove that sum of reciprocals of first $2^n$ natural nos is always greater than $\frac{n+1}{2}$

Published on 25 Mar 2026 - 12:50

score 27 · Answer 15 · 2026-04-14 12:29:20

27

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Given the variables of a summation symbol can you find the other variables?

Published on 14 Apr 2026 - 12:29

List Question

Compute $\sum_{x\in\mathcal{N}}\sum_{y\in\mathcal{N}}\frac{1}{x+y+1}$

Sum of reciprocals of perimeters of primitive Pythagorean triples

Show that $\frac{1}{x^x}$ is continuous on $[0,1]$, and find its integral on this range.

Proving $\pi=(27S-36)/(8\sqrt{3})$, where $S=\sum_{n=0}^\infty\frac{\left(\left\lfloor\frac{n}{2}\right\rfloor!\right)^2}{n!}$

A summation involving the inverses of the products of the elements of subsets of a set

Finding an identity to simplify this combinatorics solution

$\sum_i \frac{1}{x^{1/2^i}}$

Solution to $\sum_{0\leq n_1\leq n_2\leq\cdots\leq n_\beta\leq\gamma}{(-1)^{n_1+n_2+\cdots+n_\beta}}$

Sum $\sum_{k=1}^n{k(k-1)}$

How to show $\sum_{i=0}^{2m} (-1)^{i}\binom{2m}{i}^{2} = (-1)^m\binom{2m}{m}$

Using integral comparison to estimate how fast the partial sums of $\sum_{k=1}^N\frac1{k^3}$ converge

A strange inequality

Question about $x \in \text{Img}(X)$

How do I prove that sum of reciprocals of first $2^n$ natural nos is always greater than $\frac{n+1}{2}$

Given the variables of a summation symbol can you find the other variables?

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