Question

Evaluate $\lim_{n \to \infty} \prod_{k=n+1}^{2n} k^{1/k}$

score 78 · Answer 1 · 2022-01-03 22:23:22

78

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Evaluate $\lim_{n \to \infty} \prod_{k=n+1}^{2n} k^{1/k}$

Published on 03 Jan 2022 - 22:23

score 55 · Answer 2 · 2022-01-10 14:47:49

55

Views

Prove that $\prod_{i\in I}X_i\cap\prod_{i\in I}Y_i=\prod_{i\in I}(X_i\cap Y_i)$

Published on 10 Jan 2022 - 14:47

score 93 · Answer 3 · 2022-01-21 17:55:14

93

Views

Solving an infinite alternating product

Published on 21 Jan 2022 - 17:55

score 93 · Answer 4 · 2022-01-22 11:35:54

The maps $f_n: \Bbb R^n \to \Bbb R^{\Bbb N}$ induce final topology $\tau$ on $\Bbb R^\infty$. Compare it with the subspace top from $\Bbb R^{\Bbb N} $

score 50 · Answer 5 · 2022-01-23 16:19:14

50

Views

Infinite product of $(1/2)\cdot(3/4)\cdot(7/8)\cdot(15/16)\cdot(31/32)\cdot\;\cdots\,$?

Published on 23 Jan 2022 - 16:19

score 49 · Answer 6 · 2022-02-02 09:22:41

49

Views

Suppose $A=\sum_{k=0}^{\infty}f(k)=B\prod_{n=0}^{\infty}g(n)$. If $A$ and $f(k)$ are known, how to find $B$ and $g(n)$?

Published on 02 Feb 2022 - 9:22

score 92 · Answer 7 · 2022-02-06 08:08:47

92

Views

Is the fact that $\int_{0}^{\infty} \cos(2x)\prod_{n=1}^{\infty} \cos\big(\frac{x}{n}\big) dx\approx \frac{\pi}{8}$ a pure numerical coincidence?

Published on 06 Feb 2022 - 8:08

score 124 · Answer 8 · 2022-02-08 05:47:18

124

Views

How to compute $\lim_{n \to \infty} \frac{1}{n} \left[(n^2 +1^2)(n^2+2^2)^2 \cdots (n^2 + n^2)^n \right]^{\frac{1}{n^2}}$

Published on 08 Feb 2022 - 5:47

score 208 · Answer 9 · 2022-02-08 15:23:00

208

Views

Is the following infinite product of fractions of linear factors equal to an exponential function or not?

Published on 08 Feb 2022 - 15:23

score 116 · Answer 10 · 2026-03-28 20:22:20

116

Views

Two competing definitions of the direct sum of vector spaces

Published on 28 Mar 2026 - 20:22

score 113 · Answer 11 · 2022-02-26 10:23:59

113

Views

Convergence of $\prod_{n=1}^{\infty} (1 - z^n)$ when $|z| = 1$

Published on 26 Feb 2022 - 10:23

score 114 · Answer 12 · 2022-03-02 06:26:40

114

Views

Proving that $\prod_{n=0}^\infty (1 + x^{2^{n}}) = \frac{1}{1-x}$

Published on 02 Mar 2022 - 6:26

score 89 · Answer 13 · 2022-03-05 22:43:39

89

Views

What can we say about the infinite product $\prod_{n = 1}^\infty (1 - x/n^p)$?

Published on 05 Mar 2022 - 22:43

score 32 · Answer 14 · 2022-03-11 06:04:28

32

Views

Solution verification of $\prod_{n=1}^{\infty} a_n$ and $\prod_{n=1}^{\infty} b_n$ convergent, what can be said about $\prod_{n=1}^{\infty} a_n^2$

Published on 11 Mar 2022 - 6:04

score 41 · Answer 15 · 2022-03-12 05:49:34

41

Views

calculate limitation of product of expression

Published on 12 Mar 2022 - 5:49

List Question

Evaluate $\lim_{n \to \infty} \prod_{k=n+1}^{2n} k^{1/k}$

Prove that $\prod_{i\in I}X_i\cap\prod_{i\in I}Y_i=\prod_{i\in I}(X_i\cap Y_i)$

Solving an infinite alternating product

The maps $f_n: \Bbb R^n \to \Bbb R^{\Bbb N}$ induce final topology $\tau$ on $\Bbb R^\infty$. Compare it with the subspace top from $\Bbb R^{\Bbb N} $

Infinite product of $(1/2)\cdot(3/4)\cdot(7/8)\cdot(15/16)\cdot(31/32)\cdot\;\cdots\,$?

Suppose $A=\sum_{k=0}^{\infty}f(k)=B\prod_{n=0}^{\infty}g(n)$. If $A$ and $f(k)$ are known, how to find $B$ and $g(n)$?

Is the fact that $\int_{0}^{\infty} \cos(2x)\prod_{n=1}^{\infty} \cos\big(\frac{x}{n}\big) dx\approx \frac{\pi}{8}$ a pure numerical coincidence?

How to compute $\lim_{n \to \infty} \frac{1}{n} \left[(n^2 +1^2)(n^2+2^2)^2 \cdots (n^2 + n^2)^n \right]^{\frac{1}{n^2}}$

Is the following infinite product of fractions of linear factors equal to an exponential function or not?

Two competing definitions of the direct sum of vector spaces

Convergence of $\prod_{n=1}^{\infty} (1 - z^n)$ when $|z| = 1$

Proving that $\prod_{n=0}^\infty (1 + x^{2^{n}}) = \frac{1}{1-x}$

What can we say about the infinite product $\prod_{n = 1}^\infty (1 - x/n^p)$?

Solution verification of $\prod_{n=1}^{\infty} a_n$ and $\prod_{n=1}^{\infty} b_n$ convergent, what can be said about $\prod_{n=1}^{\infty} a_n^2$

calculate limitation of product of expression

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