Question

Rearrange finite product to isolate variable

score 68 · Answer 1 · 2020-06-21 15:34:43

68

Views

Rearrange finite product to isolate variable

Published on 21 Jun 2020 - 15:34

score 107 · Answer 2 · 2020-06-22 19:01:13

107

Views

Prove that $\prod_{k=2}^{99}\frac{k^{3}-1}{k^{3}+1}$ is greater than $\frac{2}{3}$.

Published on 22 Jun 2020 - 19:01

score 958 · Answer 3 · 2020-06-23 11:58:38

958

Views

Excluding a specific index when writing out a sum

Published on 23 Jun 2020 - 11:58

score 78 · Answer 4 · 2020-06-23 16:26:45

78

Views

Any hints for analysing $\prod_{i=1}^n\big(1 + \alpha(-1)^i/\sqrt i\big)$?

Published on 23 Jun 2020 - 16:26

score 38 · Answer 5 · 2020-06-26 01:24:28

38

Views

Approximating $f(n,k,c) = \prod_{i=0}^{k-1} \frac{n-ic}{n-i}.$

Published on 26 Jun 2020 - 1:24

score 110 · Answer 6 · 2026-03-30 11:20:28

110

Views

Is there a way to approximate the terms of $\frac{\left(2n\right)!}{\left(2^nn!\right)^2}$ for successive $n$ as $n$ becomes large?

Published on 30 Mar 2026 - 11:20

score 50 · Answer 7 · 2026-03-29 08:44:34

50

Views

Help with straight-forward proof of product involving Gamma functions

Published on 29 Mar 2026 - 8:44

score 66 · Answer 8 · 2020-07-02 04:49:09

66

Views

Prove that $\prod_{i=1}^{n}i^{n+1-i}=\prod_{i=1}^{n}(n+1-i)^i$ by induction.

Published on 02 Jul 2020 - 4:49

score 217 · Answer 9 · 2026-03-28 14:37:45

217

Views

Product of two generalized hypergeometric functions ${}_1F_2 \times {}_1F_2$

Published on 28 Mar 2026 - 14:37

score 65 · Answer 10 · 2020-07-04 01:49:11

65

Views

Is there a nice way to represent $\prod_{m=1}^{2^{n-1}} \cos\left(2^{m-1} x\right)$?

Published on 04 Jul 2020 - 1:49

score 66 · Answer 11 · 2026-03-25 13:46:46

66

Views

Prove of $\prod_{d|n} (\mu(d)(\mu(d) + 3) + 4) = 4^{d(n)}$

Published on 25 Mar 2026 - 13:46

score 52 · Answer 12 · 2026-03-26 01:01:19

52

Views

Finite Jacobi triple product

Published on 26 Mar 2026 - 1:01

score 39 · Answer 13 · 2020-07-05 18:48:59

39

Views

Convergence of the product $\prod_{n=2}^{\infty} \left(1+\frac{n!}{n^n}\right)$

Published on 05 Jul 2020 - 18:48

score 127 · Answer 14 · 2020-07-07 12:29:33

127

Views

Approximation of weighted sum (sum of a product)

Published on 07 Jul 2020 - 12:29

score 170 · Answer 15 · 2020-07-09 05:38:28

170

Views

Remainder when $\prod_{n=1}^{100}(1- n^{2} +n^{4})$ is divided by $101$

Published on 09 Jul 2020 - 5:38

List Question

Rearrange finite product to isolate variable

Prove that $\prod_{k=2}^{99}\frac{k^{3}-1}{k^{3}+1}$ is greater than $\frac{2}{3}$.

Excluding a specific index when writing out a sum

Any hints for analysing $\prod_{i=1}^n\big(1 + \alpha(-1)^i/\sqrt i\big)$?

Approximating $f(n,k,c) = \prod_{i=0}^{k-1} \frac{n-ic}{n-i}.$

Is there a way to approximate the terms of $\frac{\left(2n\right)!}{\left(2^nn!\right)^2}$ for successive $n$ as $n$ becomes large?

Help with straight-forward proof of product involving Gamma functions

Prove that $\prod_{i=1}^{n}i^{n+1-i}=\prod_{i=1}^{n}(n+1-i)^i$ by induction.

Product of two generalized hypergeometric functions ${}_1F_2 \times {}_1F_2$

Is there a nice way to represent $\prod_{m=1}^{2^{n-1}} \cos\left(2^{m-1} x\right)$?

Prove of $\prod_{d|n} (\mu(d)(\mu(d) + 3) + 4) = 4^{d(n)}$

Finite Jacobi triple product

Convergence of the product $\prod_{n=2}^{\infty} \left(1+\frac{n!}{n^n}\right)$

Approximation of weighted sum (sum of a product)

Remainder when $\prod_{n=1}^{100}(1- n^{2} +n^{4})$ is divided by $101$

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