Question

Convergence of $\sum_{n=1}^{\infty}\left(\left(\sqrt{n}\right)\left(n^{\alpha\cos(\frac{1}{n})}-n-\cos\left(\frac{1}{n}\right)\right)\right)^{-1}$

score 144 · Answer 1 · 2026-04-17 06:12:28

Convergence of $\sum_{n=1}^{\infty}\left(\left(\sqrt{n}\right)\left(n^{\alpha\cos(\frac{1}{n})}-n-\cos\left(\frac{1}{n}\right)\right)\right)^{-1}$

score 398 · Answer 2 · 2026-05-10 13:48:44

398

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What is this function related with continued fractions?

Published on 10 May 2026 - 13:48

score 109 · Answer 3 · 2026-04-10 18:43:09

109

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Composite numbers among a sequence

Published on 10 Apr 2026 - 18:43

score 368 · Answer 4 · 2026-04-13 20:07:26

368

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uniform convergence of exponential function on open interval

Published on 13 Apr 2026 - 20:07

score 91 · Answer 5 · 2026-04-16 22:59:51

91

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$\frac{a_{m+n}+a_{|m-n|}}{2}\leqslant a_m+a_n$ and the inequality $\limsup_{n\to\infty}\frac{a_n}{n^2}\leqslant\frac{a_k}{k^2}$

Published on 16 Apr 2026 - 22:59

score 116 · Answer 6 · 2026-04-16 19:32:46

116

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If $\frac {a_{(n+1)} }{a_n} < \frac {n^2}{(n+1)^2}$ and if $a_n > 0$ for all n . $\sum a_n$ converges or not

Published on 16 Apr 2026 - 19:32

score 181 · Answer 7 · 2026-04-15 21:00:50

181

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Evaluating an infinite sum q-series

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score 966 · Answer 8 · 2026-04-13 13:39:57

966

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Limit Comparison Test for Series when n is in the Exponent

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score 45 · Answer 9 · 2026-04-11 10:51:30

45

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score 34 · Answer 10 · 2026-04-14 00:51:02

34

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Convergence of the following series(hypergeomteric)

Published on 14 Apr 2026 - 0:51

score 60 · Answer 11 · 2026-05-10 20:53:09

60

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Can $1+\prod_{i=1}^n a_i$ be prime for all $n$?

Published on 10 May 2026 - 20:53

score 305 · Answer 12 · 2026-04-15 06:55:53

305

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Manipulating the Fourier series of $x^2$ to find the sum of a particular series

Published on 15 Apr 2026 - 6:55

score 116 · Answer 13 · 2026-05-16 08:05:28

116

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Finding $\lim_{n \to \infty} n (e^{1/n} - 1)$

Published on 16 May 2026 - 8:05

score 66 · Answer 14 · 2026-05-16 09:06:30

66

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let $a_{1} = 0, a_{2} =1$ and $a_{n+2} = \frac{(n+2)a_{n+1} - a_{n}}{n+1}$. Prove that $\lim\limits_{n \to +\infty} a_{n} = e$

Published on 16 May 2026 - 9:06

score 161 · Answer 15 · 2026-05-05 20:10:16

161

Views

How do I prove that such a sequence exists?

Published on 05 May 2026 - 20:10

List Question

Convergence of $\sum_{n=1}^{\infty}\left(\left(\sqrt{n}\right)\left(n^{\alpha\cos(\frac{1}{n})}-n-\cos\left(\frac{1}{n}\right)\right)\right)^{-1}$

What is this function related with continued fractions?

Composite numbers among a sequence

uniform convergence of exponential function on open interval

$\frac{a_{m+n}+a_{|m-n|}}{2}\leqslant a_m+a_n$ and the inequality $\limsup_{n\to\infty}\frac{a_n}{n^2}\leqslant\frac{a_k}{k^2}$

If $\frac {a_{(n+1)} }{a_n} < \frac {n^2}{(n+1)^2}$ and if $a_n > 0$ for all n . $\sum a_n$ converges or not

Evaluating an infinite sum q-series

Limit Comparison Test for Series when n is in the Exponent

Series Question (Sum to infinity) & Finding the smallest value

Convergence of the following series(hypergeomteric)

Can $1+\prod_{i=1}^n a_i$ be prime for all $n$?

Manipulating the Fourier series of $x^2$ to find the sum of a particular series

Finding $\lim_{n \to \infty} n (e^{1/n} - 1)$

let $a_{1} = 0, a_{2} =1$ and $a_{n+2} = \frac{(n+2)a_{n+1} - a_{n}}{n+1}$. Prove that $\lim\limits_{n \to +\infty} a_{n} = e$

How do I prove that such a sequence exists?

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