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Limit of AM/GM ratio for large collections of numbers

score 108 · Answer 1 · 2026-04-09 05:31:16

108

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Limit of AM/GM ratio for large collections of numbers

Published on 09 Apr 2026 - 5:31

score 76 · Answer 2 · 2026-03-24 22:01:56

76

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The limit of $2\frac{\sin\left(\frac{M\theta_{k}}{2}\right)\cos\left(\frac{1}{2}(1+M)\theta_{k}\right)}{\sin\left(\frac{\theta_{k}}{2}\right)} $

Published on 24 Mar 2026 - 22:01

score 2.4k · Answer 3 · 2026-04-09 17:40:31

2.4k

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Calculate limit with L'Hopital's rule

Published on 09 Apr 2026 - 17:40

score 277 · Answer 4 · 2026-04-02 08:12:02

277

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Evaluating a limit of a summation by expressing it as a Riemann's sum

Published on 02 Apr 2026 - 8:12

score 93 · Answer 5 · 2026-04-09 02:39:19

93

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Calculating an integral using the limit definition

Published on 09 Apr 2026 - 2:39

score 176 · Answer 6 · 2026-03-24 19:52:33

176

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Show that $\sqrt{|x| + |y|}$ is differentiable at nonzero points

Published on 24 Mar 2026 - 19:52

score 255 · Answer 7 · 2026-04-08 20:51:18

255

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Limit of a Sequence involving factorials

Published on 08 Apr 2026 - 20:51

score 850 · Answer 8 · 2026-03-26 23:20:11

850

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Divergence in the Complex Plane

Published on 26 Mar 2026 - 23:20

score 104 · Answer 9 · 2026-04-08 22:43:48

104

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quotients of Dedekind eta at irrational points on the boundary

Published on 08 Apr 2026 - 22:43

score 442 · Answer 10 · 2018-01-21 10:55:13

442

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$\forall\epsilon>0, \exists N\in\Bbb N$ such that $\forall n>m\ge N, a_n-a_m<\epsilon$. Prove that $a_n$ converges to a real limit or to $-\infty$

Published on 21 Jan 2018 - 10:55

score 67 · Answer 11 · 2026-04-10 01:33:16

67

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How to solve $\lim_\limits{x\to1} \frac{\sqrt{2x-1} -1}{x^2-1}$?

Published on 10 Apr 2026 - 1:33

score 921 · Answer 12 · 2026-03-25 03:02:38

921

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Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $

Published on 25 Mar 2026 - 3:02

score 37 · Answer 13 · 2026-04-06 23:52:50

37

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Sparse sets $S$ of integers such that $\frac{1}{x^2}\sum_{s\in S, s\le x}s\to 0$

Published on 06 Apr 2026 - 23:52

score 1.8k · Answer 14 · 2018-01-21 21:59:02

1.8k

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Does the series $\sum 2^n \sin(\frac{\pi}{3^n})$ converge?

Published on 21 Jan 2018 - 21:59

score 149 · Answer 15 · 2026-03-24 22:09:47

149

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Need help to solve this limit (Calculus) without L'Hospital's Rule

Published on 24 Mar 2026 - 22:09

List Question

Limit of AM/GM ratio for large collections of numbers

The limit of $2\frac{\sin\left(\frac{M\theta_{k}}{2}\right)\cos\left(\frac{1}{2}(1+M)\theta_{k}\right)}{\sin\left(\frac{\theta_{k}}{2}\right)} $

Calculate limit with L'Hopital's rule

Evaluating a limit of a summation by expressing it as a Riemann's sum

Calculating an integral using the limit definition

Show that $\sqrt{|x| + |y|}$ is differentiable at nonzero points

Limit of a Sequence involving factorials

Divergence in the Complex Plane

quotients of Dedekind eta at irrational points on the boundary

$\forall\epsilon>0, \exists N\in\Bbb N$ such that $\forall n>m\ge N, a_n-a_m<\epsilon$. Prove that $a_n$ converges to a real limit or to $-\infty$

How to solve $\lim_\limits{x\to1} \frac{\sqrt{2x-1} -1}{x^2-1}$?

Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $

Sparse sets $S$ of integers such that $\frac{1}{x^2}\sum_{s\in S, s\le x}s\to 0$

Does the series $\sum 2^n \sin(\frac{\pi}{3^n})$ converge?

Need help to solve this limit (Calculus) without L'Hospital's Rule

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