Question

show that $\frac {a_{N+1}}{s_{N+1}} +...+\frac {a_{N+k}}{s_{N+k}}\geq 1 -\frac {a_{N}}{s_{N+k}} $

score 146 · Answer 1 · 2026-03-27 20:25:50

146

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show that $\frac {a_{N+1}}{s_{N+1}} +...+\frac {a_{N+k}}{s_{N+k}}\geq 1 -\frac {a_{N}}{s_{N+k}} $

Published on 27 Mar 2026 - 20:25

score 1.1k · Answer 2 · 2026-03-27 19:33:38

1.1k

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Prove a strong inequality $\sum_{k=1}^n\frac{k}{a_1+a_2+\cdots+a_k}\le\left(2-\frac{7\ln 2}{8\ln n}\right)\sum_{k=1}^n\frac 1{a_k}$

Published on 27 Mar 2026 - 19:33

score 200 · Answer 3 · 2026-03-25 06:09:00

200

Views

A proof on multinomial roots

Published on 25 Mar 2026 - 6:09

score 82 · Answer 4 · 2026-03-25 06:01:28

82

Views

Infinite summation question and i need to make an algorithm for finding the summation?

Published on 25 Mar 2026 - 6:01

score 62 · Answer 5 · 2026-03-25 23:10:09

62

Views

What is the general term of $\sum_{i=2}^{n/2} (n-i)!$?

Published on 25 Mar 2026 - 23:10

score 146 · Answer 6 · 2026-03-25 01:18:13

146

Views

Computing the value of $\frac{1}{3^2+1} + \frac{1}{4^2+2} + \frac{1}{5^2+3}\ldots=$?

Published on 25 Mar 2026 - 1:18

score 92 · Answer 7 · 2018-10-13 15:43:38

92

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Calculate $\sum_{n\ge2}\log\left(1-\frac1{n^2}\right)$

Published on 13 Oct 2018 - 15:43

score 41 · Answer 8 · 2026-03-28 03:35:00

41

Views

Finding the geometric sum of this recurrence

Published on 28 Mar 2026 - 3:35

score 250 · Answer 9 · 2026-03-29 07:29:07

250

Views

$\sum\limits_{k=1}^nk^r = \frac{1}{1+r}n^{r+1}+a_rn^r +....+a_1n$

Published on 29 Mar 2026 - 7:29

score 213 · Answer 10 · 2026-03-25 04:43:29

213

Views

Show that $\frac {1}{3+x^2+y^2} + \frac {1}{3+y^2+z^2} +\frac{1} {3+x^2+z^2}\leq \frac {3}{5} . $

Published on 25 Mar 2026 - 4:43

score 255 · Answer 11 · 2026-03-27 08:38:32

255

Views

Solving for mixture coefficients in Gaussian Mixture Model

Published on 27 Mar 2026 - 8:38

score 214 · Answer 12 · 2026-03-25 10:00:09

214

Views

How Can I Represent These Progressions in Sigma Notation?

Published on 25 Mar 2026 - 10:00

score 1.5k · Answer 13 · 2026-03-26 19:20:56

1.5k

Views

Prove $\ 1<\frac{1}{n+1}+\frac{1}{n+2}+ ... + \frac{1}{3n+1}<2 $ using Cauchy-Schwarz

Published on 26 Mar 2026 - 19:20

score 63 · Answer 14 · 2026-03-25 11:09:44

63

Views

Matrix and two vectors product

Published on 25 Mar 2026 - 11:09

score 61 · Answer 15 · 2018-10-15 04:03:51

61

Views

Summing a Sequence

Published on 15 Oct 2018 - 4:03

List Question

show that $\frac {a_{N+1}}{s_{N+1}} +...+\frac {a_{N+k}}{s_{N+k}}\geq 1 -\frac {a_{N}}{s_{N+k}} $

Prove a strong inequality $\sum_{k=1}^n\frac{k}{a_1+a_2+\cdots+a_k}\le\left(2-\frac{7\ln 2}{8\ln n}\right)\sum_{k=1}^n\frac 1{a_k}$

A proof on multinomial roots

Infinite summation question and i need to make an algorithm for finding the summation?

What is the general term of $\sum_{i=2}^{n/2} (n-i)!$?

Computing the value of $\frac{1}{3^2+1} + \frac{1}{4^2+2} + \frac{1}{5^2+3}\ldots=$?

Calculate $\sum_{n\ge2}\log\left(1-\frac1{n^2}\right)$

Finding the geometric sum of this recurrence

$\sum\limits_{k=1}^nk^r = \frac{1}{1+r}n^{r+1}+a_rn^r +....+a_1n$

Show that $\frac {1}{3+x^2+y^2} + \frac {1}{3+y^2+z^2} +\frac{1} {3+x^2+z^2}\leq \frac {3}{5} . $

Solving for mixture coefficients in Gaussian Mixture Model

How Can I Represent These Progressions in Sigma Notation?

Prove $\ 1<\frac{1}{n+1}+\frac{1}{n+2}+ ... + \frac{1}{3n+1}<2 $ using Cauchy-Schwarz

Matrix and two vectors product

Summing a Sequence

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