Question

Create sequence with equal distance between items

score 238 · Answer 1 · 2026-04-29 04:48:35

238

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Create sequence with equal distance between items

Published on 29 Apr 2026 - 4:48

score 55 · Answer 2 · 2026-04-12 16:34:35

55

Views

Strategy or software for representing infinite series in sigma form

Published on 12 Apr 2026 - 16:34

score 129 · Answer 3 · 2026-04-13 09:12:58

129

Views

Showing that $a_n \in \ell^{\infty}$

Published on 13 Apr 2026 - 9:12

score 890 · Answer 4 · 2026-04-09 12:02:05

890

Views

Uniform convergence of piecewise sequence of functions

Published on 09 Apr 2026 - 12:02

score 66 · Answer 5 · 2026-04-11 00:38:48

66

Views

Stuck Simplifying for a Fibonacci Series

Published on 11 Apr 2026 - 0:38

score 282 · Answer 6 · 2026-04-16 01:45:32

282

Views

Sequence of Partial Sums is Bounded and Monotone

Published on 16 Apr 2026 - 1:45

score 406 · Answer 7 · 2026-04-14 05:22:16

406

Views

Prove that $f_n$ does not converge uniformly to any function $f\colon(-1,1)\to {\Bbb R}$.

Published on 14 Apr 2026 - 5:22

score 139 · Answer 8 · 2026-04-15 05:14:50

Find the largest $n \in \mathbb{N_+} $ such that $\{ (2+\sqrt 2)^n\} < \frac{7}{8}$, where $\{x\}$ denotes the fractional part of $x$.

score 89 · Answer 9 · 2026-04-16 14:12:06

89

Views

How to show that $\ln\left(\sin(\pi x)/(\pi x)\right)=\sum_{n=1}^{+\infty}\ln\left(1-x^2/n^2\right)$

Published on 16 Apr 2026 - 14:12

score 54 · Answer 10 · 2026-04-14 23:47:09

54

Views

Does $|a_{k+1}|\leq|a_k|$ and $\sum_{k=0}^\infty|a_{k+1}-a_{k}|^2<\infty$ imply $\sum_{k=0}^\infty|a_{k+1}-a_{k}|<\infty$?

Published on 14 Apr 2026 - 23:47

score 127 · Answer 11 · 2026-04-15 13:13:17

127

Views

A nested $\sin(x)$ sequence

Published on 15 Apr 2026 - 13:13

score 25 · Answer 12 · 2026-04-14 13:28:41

25

Views

Test $x_n = (n+i\pi)^n n^{-n + 1/n}$ for convergence and give its limit if possible.

Published on 14 Apr 2026 - 13:28

score 53 · Answer 13 · 2026-04-15 13:46:12

53

Views

Test $x_n=\frac{n^2 e^{-\sqrt{n}}}{\cos(1/n)}$ for convergence and give its limit if possible.

Published on 15 Apr 2026 - 13:46

score 50 · Answer 14 · 2026-04-18 22:33:51

50

Views

Convergence of a Series with Infinitely Many Increasing Terms

Published on 18 Apr 2026 - 22:33

score 788 · Answer 15 · 2026-04-15 00:51:14

788

Views

Summation of $\sum_{r=1}^{n} \frac{\cos (2rx)}{\sin((2r+1)x \sin((2r-1)x}$

Published on 15 Apr 2026 - 0:51

List Question

Create sequence with equal distance between items

Strategy or software for representing infinite series in sigma form

Showing that $a_n \in \ell^{\infty}$

Uniform convergence of piecewise sequence of functions

Stuck Simplifying for a Fibonacci Series

Sequence of Partial Sums is Bounded and Monotone

Prove that $f_n$ does not converge uniformly to any function $f\colon(-1,1)\to {\Bbb R}$.

Find the largest $n \in \mathbb{N_+} $ such that $\{ (2+\sqrt 2)^n\} < \frac{7}{8}$, where $\{x\}$ denotes the fractional part of $x$.

How to show that $\ln\left(\sin(\pi x)/(\pi x)\right)=\sum_{n=1}^{+\infty}\ln\left(1-x^2/n^2\right)$

Does $|a_{k+1}|\leq|a_k|$ and $\sum_{k=0}^\infty|a_{k+1}-a_{k}|^2<\infty$ imply $\sum_{k=0}^\infty|a_{k+1}-a_{k}|<\infty$?

A nested $\sin(x)$ sequence

Test $x_n = (n+i\pi)^n n^{-n + 1/n}$ for convergence and give its limit if possible.

Test $x_n=\frac{n^2 e^{-\sqrt{n}}}{\cos(1/n)}$ for convergence and give its limit if possible.

Convergence of a Series with Infinitely Many Increasing Terms

Summation of $\sum_{r=1}^{n} \frac{\cos (2rx)}{\sin((2r+1)x \sin((2r-1)x}$

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