Question

Convergence of $\sum_{n=1}^{\infty}(-n)^{\lfloor\alpha\rfloor}\frac{\sin^3\left(\frac{1}{n}\right)}{\left(\log(n)\right)^{\alpha-1}}$

score 80 · Answer 1 · 2026-04-16 01:38:42

80

Views

Convergence of $\sum_{n=1}^{\infty}(-n)^{\lfloor\alpha\rfloor}\frac{\sin^3\left(\frac{1}{n}\right)}{\left(\log(n)\right)^{\alpha-1}}$

Published on 16 Apr 2026 - 1:38

score 75 · Answer 2 · 2026-04-15 19:13:05

75

Views

Let $0 < a \leq 1$ and $s_1 = a/2$ , $2s_{n+1} = s_n^2 + a$ , Then how to show that the sequence is convergent.

Published on 15 Apr 2026 - 19:13

score 136 · Answer 3 · 2026-04-13 05:51:09

136

Views

A prime’s square dividing a sum of a geometric sequence

Published on 13 Apr 2026 - 5:51

score 117 · Answer 4 · 2026-05-10 15:03:16

117

Views

Double integral over fractional part of Einstein-like velocity sum $\int_0^1 \int_0^1 \{\frac{u+v}{1-u v}\} \,dudv$

Published on 10 May 2026 - 15:03

score 50 · Answer 5 · 2026-04-09 08:28:51

50

Views

How to sum with previous values multiplied on %?

Published on 09 Apr 2026 - 8:28

score 1.2k · Answer 6 · 2026-04-12 13:44:05

1.2k

Views

Solve three variables that are consecutive terms in a geometric suite?

Published on 12 Apr 2026 - 13:44

score 96 · Answer 7 · 2026-05-16 04:21:44

96

Views

Proving that the limit of the following sequence $\frac {\sqrt {n}}{1 + \sqrt{n}}$ when $n \rightarrow \infty$ is 1.

Published on 16 May 2026 - 4:21

score 223 · Answer 8 · 2026-04-12 08:32:12

223

Views

Does the sum of $\sum_{n=1}^{\infty}{\frac{2}{n^2+2n}}$ depend at which $n$ the series starts?

Published on 12 Apr 2026 - 8:32

score 183 · Answer 9 · 2026-04-16 08:21:23

183

Views

Pointwise, uniform, normal and $L^p$ convergence of $\sum\limits_{n=1}^{\infty}\frac{e^{-nx}}{1+n^2}$

Published on 16 Apr 2026 - 8:21

score 1k · Answer 10 · 2026-04-09 13:57:54

1k

Views

How to find fourth term a of geometric series using sum of first three terms and second term?

Published on 09 Apr 2026 - 13:57

score 66 · Answer 11 · 2026-04-17 10:52:48

66

Views

If $\{b_{n}\}$ is obtained by deleting the first $k$ members of $\{a_{n}\}$, then $\{b_{n}\}$ is convergent iff $\{a_{n}\}$ is convergent.

Published on 17 Apr 2026 - 10:52

score 49 · Answer 12 · 2026-04-11 06:40:59

49

Views

Link infinite series to finite series

Published on 11 Apr 2026 - 6:40

score 80 · Answer 13 · 2026-05-16 04:21:44

80

Views

Prove that the limit of the following sequence $\frac{n^3 + 2}{n^2 + 3}$ diverges to $+ \infty$.

Published on 16 May 2026 - 4:21

score 217 · Answer 14 · 2026-05-13 06:05:20

217

Views

Limit of sum of sequences at infinity

Published on 13 May 2026 - 6:05

score 92 · Answer 15 · 2026-05-10 16:10:16

92

Views

Geometric series: two ways to tackle same problem giving me issues

Published on 10 May 2026 - 16:10

List Question

Convergence of $\sum_{n=1}^{\infty}(-n)^{\lfloor\alpha\rfloor}\frac{\sin^3\left(\frac{1}{n}\right)}{\left(\log(n)\right)^{\alpha-1}}$

Let $0 < a \leq 1$ and $s_1 = a/2$ , $2s_{n+1} = s_n^2 + a$ , Then how to show that the sequence is convergent.

A prime’s square dividing a sum of a geometric sequence

Double integral over fractional part of Einstein-like velocity sum $\int_0^1 \int_0^1 \{\frac{u+v}{1-u v}\} \,dudv$

How to sum with previous values multiplied on %?

Solve three variables that are consecutive terms in a geometric suite?

Proving that the limit of the following sequence $\frac {\sqrt {n}}{1 + \sqrt{n}}$ when $n \rightarrow \infty$ is 1.

Does the sum of $\sum_{n=1}^{\infty}{\frac{2}{n^2+2n}}$ depend at which $n$ the series starts?

Pointwise, uniform, normal and $L^p$ convergence of $\sum\limits_{n=1}^{\infty}\frac{e^{-nx}}{1+n^2}$

How to find fourth term a of geometric series using sum of first three terms and second term?

If $\{b_{n}\}$ is obtained by deleting the first $k$ members of $\{a_{n}\}$, then $\{b_{n}\}$ is convergent iff $\{a_{n}\}$ is convergent.

Link infinite series to finite series

Prove that the limit of the following sequence $\frac{n^3 + 2}{n^2 + 3}$ diverges to $+ \infty$.

Limit of sum of sequences at infinity

Geometric series: two ways to tackle same problem giving me issues

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