Question

closed form of $\prod_1^n (x+k)$

score 91 · Answer 1 · 2023-03-04 21:30:20

91

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closed form of $\prod_1^n (x+k)$

Published on 04 Mar 2023 - 21:30

score 96 · Answer 2 · 2023-03-10 17:59:00

96

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How to prove $\prod_{k=1}^n (1+a_k)\leq \sum_{j=0}^n\left(\sum_{k=1}^n a_k\right)^j$

Published on 10 Mar 2023 - 17:59

score 36 · Answer 3 · 2023-03-12 03:25:20

36

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How to calculate this limit by stolz theorem

Published on 12 Mar 2023 - 3:25

score 105 · Answer 4 · 2023-03-25 14:38:50

105

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Equation involving double sum and product

Published on 25 Mar 2023 - 14:38

score 41 · Answer 5 · 2026-03-27 00:05:24

41

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Simplifying the product of $(x-x_j)$'s when $x_k$ has multiplicty $\geq 2$

Published on 27 Mar 2026 - 0:05

score 63 · Answer 6 · 2023-03-27 14:02:46

63

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Convergence of an infinite product using logarithm

Published on 27 Mar 2023 - 14:02

score 94 · Answer 7 · 2023-03-29 05:00:12

94

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If $N$ and $K$ are normal subgroups of a group $G$ such that $G=MN$ and $M\cap N=\langle e \rangle$ then $G=M\times N$.

Published on 29 Mar 2023 - 5:00

score 175 · Answer 8 · 2026-03-27 13:24:29

175

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Prove or (dis)prove that : $f(x,y)\geq 0$

Published on 27 Mar 2026 - 13:24

score 128 · Answer 9 · 2026-03-28 11:54:15

128

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What is $\lim_{x\to \infty}f(x)=\lim_{x\to \infty}\int_{0}^{x}\prod_{n=1}^{\infty}\left(1-e^{-t-n}\right)dt-x+1$

Published on 28 Mar 2026 - 11:54

score 76 · Answer 10 · 2026-03-28 13:35:41

76

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Difficult limit $\lim_{x\to 0}f(x)=^?e$

Published on 28 Mar 2026 - 13:35

score 58 · Answer 11 · 2023-04-06 09:53:58

58

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Prove or (dis)prove $\prod_{n=1}^{\infty}\left(1+e^{-n}\right)+\lim_{x\to 0}\ln\left(f\left(x\right)\right)=1$

Published on 06 Apr 2023 - 9:53

score 92 · Answer 12 · 2023-04-07 22:17:10

92

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Product Inequalites

Published on 07 Apr 2023 - 22:17

score 25 · Answer 13 · 2023-04-11 10:43:46

25

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can you swap the boundaries of an empty product?

Published on 11 Apr 2023 - 10:43

score 136 · Answer 14 · 2023-04-14 00:14:20

136

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How can I prove this formula: $\sum_{a_1+a_2+\cdots +a_m\le n}\prod_{i=1}^ma_i=\binom{n+m}{2m}$?

Published on 14 Apr 2023 - 0:14

score 94 · Answer 15 · 2023-04-25 03:24:54

Help me Prove $\prod_{k=1}^{2n}k=4^{n}\sec\left(\pi n\right)\left(\prod_{k=0}^{n-1}\left(-\frac{1}{2}-k\right)\right)\left(\prod_{k=1}^{n}k\right)$

List Question

closed form of $\prod_1^n (x+k)$

How to prove $\prod_{k=1}^n (1+a_k)\leq \sum_{j=0}^n\left(\sum_{k=1}^n a_k\right)^j$

How to calculate this limit by stolz theorem

Equation involving double sum and product

Simplifying the product of $(x-x_j)$'s when $x_k$ has multiplicty $\geq 2$

Convergence of an infinite product using logarithm

If $N$ and $K$ are normal subgroups of a group $G$ such that $G=MN$ and $M\cap N=\langle e \rangle$ then $G=M\times N$.

Prove or (dis)prove that : $f(x,y)\geq 0$

What is $\lim_{x\to \infty}f(x)=\lim_{x\to \infty}\int_{0}^{x}\prod_{n=1}^{\infty}\left(1-e^{-t-n}\right)dt-x+1$

Difficult limit $\lim_{x\to 0}f(x)=^?e$

Prove or (dis)prove $\prod_{n=1}^{\infty}\left(1+e^{-n}\right)+\lim_{x\to 0}\ln\left(f\left(x\right)\right)=1$

Product Inequalites

can you swap the boundaries of an empty product?

How can I prove this formula: $\sum_{a_1+a_2+\cdots +a_m\le n}\prod_{i=1}^ma_i=\binom{n+m}{2m}$?

Help me Prove $\prod_{k=1}^{2n}k=4^{n}\sec\left(\pi n\right)\left(\prod_{k=0}^{n-1}\left(-\frac{1}{2}-k\right)\right)\left(\prod_{k=1}^{n}k\right)$

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