Question

Evaluating the Sum $\sum_{r=1}^L \sum_{i=1}^L \left \lfloor \frac {L}{\left(\frac {r^2+i^2}{gcd(r,i)}\right)}\right \rfloor \cdot 2r$

score 61 · Answer 1 · 2026-03-27 18:49:35

61

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Evaluating the Sum $\sum_{r=1}^L \sum_{i=1}^L \left \lfloor \frac {L}{\left(\frac {r^2+i^2}{gcd(r,i)}\right)}\right \rfloor \cdot 2r$

Published on 27 Mar 2026 - 18:49

score 448 · Answer 2 · 2026-03-29 04:48:56

448

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what is exponential generating function with n Choose k as coefficient

Published on 29 Mar 2026 - 4:48

score 76 · Answer 3 · 2026-04-01 14:22:38

76

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Proving an equality of two sums using induction for $n \in \mathbb N$

Published on 01 Apr 2026 - 14:22

score 57 · Answer 4 · 2026-03-25 05:09:42

57

Views

Series: Product of power and exponential

Published on 25 Mar 2026 - 5:09

score 143 · Answer 5 · 2026-04-01 14:23:49

143

Views

Prove that $\sum_{k=0}^{n}{\frac{1}{k!}}\leq 3$ $\forall n\in \mathbb{N}$

Published on 01 Apr 2026 - 14:23

score 49 · Answer 6 · 2019-06-06 21:16:11

49

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What is $2\sum^2_{i=1}\sum^2_{j>i}a_{ij}x_ix_j$ is equal to?

Published on 06 Jun 2019 - 21:16

score 94 · Answer 7 · 2019-06-07 05:32:10

94

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Find the value of $a_4-a_2$

Published on 07 Jun 2019 - 5:32

score 117 · Answer 8 · 2026-03-27 10:31:31

117

Views

A die is thrown $k$ times. How to determine the sum equal to $k$?

Published on 27 Mar 2026 - 10:31

score 131 · Answer 9 · 2019-06-08 12:02:44

131

Views

Equating coefficients of like terms involving a summation

Published on 08 Jun 2019 - 12:02

score 66 · Answer 10 · 2019-06-08 12:17:47

66

Views

Snails and Sums

Published on 08 Jun 2019 - 12:17

score 37 · Answer 11 · 2019-06-08 14:14:13

37

Views

Prove that $\sum_{k=0}^{\infty}{\frac{(3i)^k}{k!}}$ converges .

Published on 08 Jun 2019 - 14:14

score 71 · Answer 12 · 2026-03-25 03:02:47

71

Views

Closed form of many repeated summations of n

Published on 25 Mar 2026 - 3:02

score 130 · Answer 13 · 2019-06-09 10:54:11

130

Views

Proving integral $\int_0^1\frac{e^x-1}{x}$ is equal to $\sum_{n=1}^{\infty}\frac{1}{n \cdot n!}$

Published on 09 Jun 2019 - 10:54

score 575 · Answer 14 · 2019-06-09 13:07:43

575

Views

Prove that $\sum_{n=1}^{\infty}\log \cos \left (\frac{1}{n}\right )$ converges absolutely.

Published on 09 Jun 2019 - 13:07

score 66 · Answer 15 · 2019-06-09 15:20:41

66

Views

Compute difficult sum

Published on 09 Jun 2019 - 15:20

List Question

Evaluating the Sum $\sum_{r=1}^L \sum_{i=1}^L \left \lfloor \frac {L}{\left(\frac {r^2+i^2}{gcd(r,i)}\right)}\right \rfloor \cdot 2r$

what is exponential generating function with n Choose k as coefficient

Proving an equality of two sums using induction for $n \in \mathbb N$

Series: Product of power and exponential

Prove that $\sum_{k=0}^{n}{\frac{1}{k!}}\leq 3$ $\forall n\in \mathbb{N}$

What is $2\sum^2_{i=1}\sum^2_{j>i}a_{ij}x_ix_j$ is equal to?

Find the value of $a_4-a_2$

A die is thrown $k$ times. How to determine the sum equal to $k$?

Equating coefficients of like terms involving a summation

Snails and Sums

Prove that $\sum_{k=0}^{\infty}{\frac{(3i)^k}{k!}}$ converges .

Closed form of many repeated summations of n

Proving integral $\int_0^1\frac{e^x-1}{x}$ is equal to $\sum_{n=1}^{\infty}\frac{1}{n \cdot n!}$

Prove that $\sum_{n=1}^{\infty}\log \cos \left (\frac{1}{n}\right )$ converges absolutely.

Compute difficult sum

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