Question

Convergence of integral: $ \int_{0}^{\infty} \frac{\sin{\left(x+\frac{1}{x}\right)}}{x^{a}}\ dx $

score 71 · Answer 1 · 2019-09-02 16:48:19

71

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Convergence of integral: $ \int_{0}^{\infty} \frac{\sin{\left(x+\frac{1}{x}\right)}}{x^{a}}\ dx $

Published on 02 Sep 2019 - 16:48

score 365 · Answer 2 · 2026-03-22 03:01:55

365

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Does the series $\sum_{n=1}^{\infty}\sin\left(2\pi\sqrt{n^2+\alpha^2\sin n+(-1)^n}\right)$ converge?

Published on 22 Mar 2026 - 3:01

score 2.4k · Answer 3 · 2026-03-22 08:41:50

2.4k

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Theorem 3.54 (about certain rearrangements of a conditionally convergent series) in Baby Rudin: A couple of questions about the proof

Published on 22 Mar 2026 - 8:41

score 33 · Answer 4 · 2019-10-06 18:47:09

33

Views

Explore the series for absolute and conditional convergence

Published on 06 Oct 2019 - 18:47

score 32 · Answer 5 · 2019-10-07 07:28:18

32

Views

The series for absolute and conditional convergence

Published on 07 Oct 2019 - 7:28

score 136 · Answer 6 · 2019-10-24 03:10:14

136

Views

How to show a series is conditionally convergent

Published on 24 Oct 2019 - 3:10

score 288 · Answer 7 · 2019-11-16 16:52:02

288

Views

Is $\sum{\frac{i^{n}}{n}}$ convergent or divergent?

Published on 16 Nov 2019 - 16:52

score 67 · Answer 8 · 2019-11-21 10:40:25

67

Views

What is the limit of the nth root of a sequenc which diverges?

Published on 21 Nov 2019 - 10:40

score 499 · Answer 9 · 2019-12-20 06:05:49

499

Views

Rearrangement in proof for Euler's formula

Published on 20 Dec 2019 - 6:05

score 102 · Answer 10 · 2020-01-16 12:35:39

102

Views

How do I need to use Euler-Maclaurin summation formula to calcuate the limits $\lim S_n$?

Published on 16 Jan 2020 - 12:35

score 214 · Answer 11 · 2020-01-24 03:51:11

214

Views

Does $\iint_D \frac{x^2}{x^2+y^2} dx dy $ converge on $D= \left\{ (x, y) : x^2+y^2\leq ax \right\} $ ? If yes, what value does it converge to?

Published on 24 Jan 2020 - 3:51

score 313 · Answer 12 · 2026-02-24 02:14:18

313

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Let $f(x)$ be the $2π$-periodic function defined by $ f(x)= \begin{cases} 1+x&\,x \in \mathbb [0,π)\\ -x-2&\, x \in \mathbb [-π,0)\\ \end{cases} $

Published on 24 Feb 2026 - 2:14

score 31 · Answer 13 · 2020-02-22 08:31:16

31

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Let $\sum a_n=s$ be conditional convergent, $\sum a_{f(n)}=t\neq s$. Show $\forall\ N, \exists\ n$, such that $|n-f(n)|>N$.

Published on 22 Feb 2020 - 8:31

score 65 · Answer 14 · 2020-03-31 14:04:12

65

Views

Finding the values of x for which this series converges

Published on 31 Mar 2020 - 14:04

score 661 · Answer 15 · 2020-04-05 22:53:21

661

Views

A series conditionally convergent to 0 whose sequence of partial sums is positive.

Published on 05 Apr 2020 - 22:53

List Question

Convergence of integral: $ \int_{0}^{\infty} \frac{\sin{\left(x+\frac{1}{x}\right)}}{x^{a}}\ dx $

Does the series $\sum_{n=1}^{\infty}\sin\left(2\pi\sqrt{n^2+\alpha^2\sin n+(-1)^n}\right)$ converge?

Theorem 3.54 (about certain rearrangements of a conditionally convergent series) in Baby Rudin: A couple of questions about the proof

Explore the series for absolute and conditional convergence

The series for absolute and conditional convergence

How to show a series is conditionally convergent

Is $\sum{\frac{i^{n}}{n}}$ convergent or divergent?

What is the limit of the nth root of a sequenc which diverges?

Rearrangement in proof for Euler's formula

How do I need to use Euler-Maclaurin summation formula to calcuate the limits $\lim S_n$?

Does $\iint_D \frac{x^2}{x^2+y^2} dx dy $ converge on $D= \left\{ (x, y) : x^2+y^2\leq ax \right\} $ ? If yes, what value does it converge to?

Let $f(x)$ be the $2π$-periodic function defined by $ f(x)= \begin{cases} 1+x&\,x \in \mathbb [0,π)\\ -x-2&\, x \in \mathbb [-π,0)\\ \end{cases} $

Let $\sum a_n=s$ be conditional convergent, $\sum a_{f(n)}=t\neq s$. Show $\forall\ N, \exists\ n$, such that $|n-f(n)|>N$.

Finding the values of x for which this series converges

A series conditionally convergent to 0 whose sequence of partial sums is positive.

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