Question

Find the "region of interest" of an unknown function

score 156 · Answer 1 · 2026-03-25 22:04:37

156

Views

Find the "region of interest" of an unknown function

Published on 25 Mar 2026 - 22:04

score 389 · Answer 2 · 2018-12-10 00:12:25

389

Views

Convergence of the series $\sum_{n=1}^{\infty} \frac{\cos(n^2x)}{n}$.

Published on 10 Dec 2018 - 0:12

score 696 · Answer 3 · 2026-03-29 14:03:11

696

Views

Proving the sequence $f_{n} = \sqrt{x^{2} + 1/n}$ converges uniformly to $f(x) = |x|$ on $(-1, 1)$.

Published on 29 Mar 2026 - 14:03

score 75 · Answer 4 · 2018-12-10 01:50:27

75

Views

Proving $\sum_{k = 0}^{\infty} \frac{1}{1 + |x|^{k}}$ converges if and only if $|x| > 1$

Published on 10 Dec 2018 - 1:50

score 36 · Answer 5 · 2026-03-29 13:40:59

36

Views

Given $\lim_{n\to\infty} |a_{n}|^{1/n} = \alpha$, prove the following properties.

Published on 29 Mar 2026 - 13:40

score 33 · Answer 6 · 2026-04-08 03:48:54

33

Views

Understanding the solution key to a problem which shows that the integral of a sum equals a given value.

Published on 08 Apr 2026 - 3:48

score 126 · Answer 7 · 2018-12-10 12:45:28

126

Views

Find sequence $(a_n)$ of positive reals such that $\sum a_n$ diverges but $\sum a_n/(\ln(\ln(n)))$ converges.

Published on 10 Dec 2018 - 12:45

score 2.5k · Answer 8 · 2026-03-29 13:40:48

2.5k

Views

Radius of convergence of two power series and the sum of the power serieses

Published on 29 Mar 2026 - 13:40

score 210 · Answer 9 · 2018-12-10 19:13:22

210

Views

Show that Gamma-convergence isn't preserved under addition

Published on 10 Dec 2018 - 19:13

score 507 · Answer 10 · 2026-03-25 06:04:30

507

Views

Evaluating $1-\frac12-\frac13+\frac14+\frac15+\frac16-\cdots$

Published on 25 Mar 2026 - 6:04

score 140 · Answer 11 · 2026-03-26 03:13:32

140

Views

Show that $\limsup_{k \to \infty} 2^{-k} N_k = 0$ where $N_k$ is the number of $a_n \geq 2^{-k}$.

Published on 26 Mar 2026 - 3:13

score 303 · Answer 12 · 2018-12-11 05:09:42

303

Views

Prove $\sum\limits_{n=1}^{\infty} a_{f(n)} = \dfrac{3}{2} \ln(2) $

Published on 11 Dec 2018 - 5:09

score 71 · Answer 13 · 2026-04-09 01:54:14

71

Views

Characterization of convergence in probability

Published on 09 Apr 2026 - 1:54

score 46 · Answer 14 · 2026-03-26 00:58:52

46

Views

Prove this is a cauchy sequence

Published on 26 Mar 2026 - 0:58

score 155 · Answer 15 · 2026-03-30 18:32:56

155

Views

If the Taylor expansion of $f$ converges to $f$, prove that there are constants $C,R$ such that $f^{(k)}(x) \le C \cdot \frac{k!}{R^k}$

Published on 30 Mar 2026 - 18:32

List Question

Find the "region of interest" of an unknown function

Convergence of the series $\sum_{n=1}^{\infty} \frac{\cos(n^2x)}{n}$.

Proving the sequence $f_{n} = \sqrt{x^{2} + 1/n}$ converges uniformly to $f(x) = |x|$ on $(-1, 1)$.

Proving $\sum_{k = 0}^{\infty} \frac{1}{1 + |x|^{k}}$ converges if and only if $|x| > 1$

Given $\lim_{n\to\infty} |a_{n}|^{1/n} = \alpha$, prove the following properties.

Understanding the solution key to a problem which shows that the integral of a sum equals a given value.

Find sequence $(a_n)$ of positive reals such that $\sum a_n$ diverges but $\sum a_n/(\ln(\ln(n)))$ converges.

Radius of convergence of two power series and the sum of the power serieses

Show that Gamma-convergence isn't preserved under addition

Evaluating $1-\frac12-\frac13+\frac14+\frac15+\frac16-\cdots$

Show that $\limsup_{k \to \infty} 2^{-k} N_k = 0$ where $N_k$ is the number of $a_n \geq 2^{-k}$.

Prove $\sum\limits_{n=1}^{\infty} a_{f(n)} = \dfrac{3}{2} \ln(2) $

Characterization of convergence in probability

Prove this is a cauchy sequence

If the Taylor expansion of $f$ converges to $f$, prove that there are constants $C,R$ such that $f^{(k)}(x) \le C \cdot \frac{k!}{R^k}$

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