Question

Convergence of $\sum_{n=1}^{\infty}\bigg((2\lambda)^{3n}\ \ln\big(\cos(n^{\lambda})\big)\bigg)$, for $\lambda\leqslant0, \lambda\in\mathbb{R}$

score 63 · Answer 1 · 2026-04-13 12:29:34

63

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Convergence of $\sum_{n=1}^{\infty}\bigg((2\lambda)^{3n}\ \ln\big(\cos(n^{\lambda})\big)\bigg)$, for $\lambda\leqslant0, \lambda\in\mathbb{R}$

Published on 13 Apr 2026 - 12:29

score 174 · Answer 2 · 2026-05-14 18:04:14

174

Views

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Published on 14 May 2026 - 18:04

score 231 · Answer 3 · 2026-04-13 06:18:31

231

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score 4.1k · Answer 4 · 2026-05-10 18:19:40

4.1k

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score 317 · Answer 5 · 2026-04-16 06:26:17

317

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score 88 · Answer 6 · 2026-04-15 09:30:08

88

Views

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Published on 15 Apr 2026 - 9:30

score 46 · Answer 7 · 2026-05-11 06:10:14

46

Views

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Published on 11 May 2026 - 6:10

score 68 · Answer 8 · 2026-05-10 21:11:53

68

Views

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Published on 10 May 2026 - 21:11

score 2.7k · Answer 9 · 2026-05-03 12:06:08

2.7k

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Published on 03 May 2026 - 12:06

score 327 · Answer 10 · 2026-04-11 17:31:40

327

Views

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score 47 · Answer 11 · 2026-04-10 06:49:44

47

Views

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Published on 10 Apr 2026 - 6:49

score 158 · Answer 12 · 2026-04-16 16:33:17

158

Views

Sum of an infinite series: $1 + \frac12 - \frac13- \frac14 + \frac15 + \frac16 - \cdots$?

Published on 16 Apr 2026 - 16:33

score 448 · Answer 13 · 2026-04-12 06:50:38

448

Views

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score 452 · Answer 14 · 2026-04-13 12:19:26

452

Views

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score 126 · Answer 15 · 2026-04-16 17:22:38

126

Views

Find$\{a_{n}\}$such that $a_{n+1}=\frac{a_{n}^{2}+3}{a_{n}+1},\,a_{1}=1$

Published on 16 Apr 2026 - 17:22

List Question

Convergence of $\sum_{n=1}^{\infty}\bigg((2\lambda)^{3n}\ \ln\big(\cos(n^{\lambda})\big)\bigg)$, for $\lambda\leqslant0, \lambda\in\mathbb{R}$

Proving a formula for $\pi$

Implications of Convergence of a Series

How to write recursive formula as explicit (specifically, exponential)?

Generalized Infinite Integration by Parts

Convergence of $\sum_{n=1}^{\infty} \sin\big((-1)^n\log(1+n^{-1})+n^{-2}\big)$

This Infinite Random Sequence?

Examples of complete families of functions forming an absolutely convergent series

$100$ consecutive natural numbers with no primes

Double series rearrangement

Equality or not in definition of limits and infinity and sequences?

Sum of an infinite series: $1 + \frac12 - \frac13- \frac14 + \frac15 + \frac16 - \cdots$?

Alternating sum of inverse prime numbers

Question on a Proof of the Divergence of Harmonic Series

Find$\{a_{n}\}$such that $a_{n+1}=\frac{a_{n}^{2}+3}{a_{n}+1},\,a_{1}=1$

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