Question

Finding the limit of a recursive complex sequence

score 493 · Answer 1 · 2026-05-16 02:36:20

493

Views

Finding the limit of a recursive complex sequence

Published on 16 May 2026 - 2:36

score 300 · Answer 2 · 2026-04-16 13:32:41

300

Views

Let $\lim\limits_{n\to\infty}a_{n+1}-a_{n}=\alpha$. Show that $\lim\limits_{n\to\infty} \frac{a_n}{n}=\alpha$.

Published on 16 Apr 2026 - 13:32

score 114 · Answer 3 · 2026-05-10 15:08:26

114

Views

Convergence of double sum

Published on 10 May 2026 - 15:08

score 120 · Answer 4 · 2026-05-16 03:28:29

120

Views

How to prove that the function $f$ is continuous on $\mathbb{R}$

Published on 16 May 2026 - 3:28

score 219 · Answer 5 · 2026-04-14 03:16:58

219

Views

Series $\sum_{n=1}^\infty nx^n$

Published on 14 Apr 2026 - 3:16

score 78 · Answer 6 · 2026-05-15 04:20:44

78

Views

Prove that $x\mapsto \sum^{\infty}_{n=0}f_n(x)=\sum^{\infty}_{n=0}\frac{x^2}{(1+x^2)^n}$ does not converge uniformly on $[-1,1]$

Published on 15 May 2026 - 4:20

score 178 · Answer 7 · 2026-05-15 05:29:13

178

Views

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

Published on 15 May 2026 - 5:29

score 113 · Answer 8 · 2026-05-15 05:32:17

113

Views

Show that $\sum^{\infty}_{n=1}(-1)^{n+1}\frac{1}{n+x^4}$ is uniformly convergent on $\Bbb{R}$

Published on 15 May 2026 - 5:32

score 153 · Answer 9 · 2026-04-24 01:09:36

153

Views

Prove uniqueness of limit of convergent sequence in $\mathbb{R^n}$

Published on 24 Apr 2026 - 1:09

score 130 · Answer 10 · 2026-04-15 14:08:57

130

Views

Convergence and divergence of $\frac{a_n}{n}$ as $n\to\infty$

Published on 15 Apr 2026 - 14:08

score 251 · Answer 11 · 2026-04-15 06:50:04

251

Views

Determine the limit and give and $\epsilon-N$ proof of $\lim_{n\rightarrow\infty}\frac{3+(-4)^n}{n^2}$.

Published on 15 Apr 2026 - 6:50

score 74 · Answer 12 · 2026-04-14 16:03:21

74

Views

Solving summations of form $\sum_{i=0}^{\infty} i^kx^i$ without Differentiation and Integration

Published on 14 Apr 2026 - 16:03

score 58 · Answer 13 · 2026-04-12 22:15:45

58

Views

If $A \subset \mathbb{R}^n$ is bounded an open then every sequence of $A$ has a subsequence that converges to a point of $A$

Published on 12 Apr 2026 - 22:15

score 78 · Answer 14 · 2026-05-10 19:48:50

78

Views

About the value of $\prod\limits_{\ell=0}^j((k+1)^2-(\ell+1)^2)$ where one omits the factor $\ell=k$

Published on 10 May 2026 - 19:48

score 215 · Answer 15 · 2026-05-10 15:03:16

215

Views

If the sum of a sequence of positive rational numbers is transcendental, is the sum of every subsequence that is irrational, also transcendental?

Published on 10 May 2026 - 15:03

List Question

Finding the limit of a recursive complex sequence

Let $\lim\limits_{n\to\infty}a_{n+1}-a_{n}=\alpha$. Show that $\lim\limits_{n\to\infty} \frac{a_n}{n}=\alpha$.

Convergence of double sum

How to prove that the function $f$ is continuous on $\mathbb{R}$

Series $\sum_{n=1}^\infty nx^n$

Prove that $x\mapsto \sum^{\infty}_{n=0}f_n(x)=\sum^{\infty}_{n=0}\frac{x^2}{(1+x^2)^n}$ does not converge uniformly on $[-1,1]$

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

Show that $\sum^{\infty}_{n=1}(-1)^{n+1}\frac{1}{n+x^4}$ is uniformly convergent on $\Bbb{R}$

Prove uniqueness of limit of convergent sequence in $\mathbb{R^n}$

Convergence and divergence of $\frac{a_n}{n}$ as $n\to\infty$

Determine the limit and give and $\epsilon-N$ proof of $\lim_{n\rightarrow\infty}\frac{3+(-4)^n}{n^2}$.

Solving summations of form $\sum_{i=0}^{\infty} i^kx^i$ without Differentiation and Integration

If $A \subset \mathbb{R}^n$ is bounded an open then every sequence of $A$ has a subsequence that converges to a point of $A$

About the value of $\prod\limits_{\ell=0}^j((k+1)^2-(\ell+1)^2)$ where one omits the factor $\ell=k$

If the sum of a sequence of positive rational numbers is transcendental, is the sum of every subsequence that is irrational, also transcendental?

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