Question

Radius of convergence of $\sum_{n=0}^{\infty}\frac{x^n}{(\cos^{-1}(\sqrt{n+1}-\sqrt{n}))^n}$

score 407 · Answer 1 · 2026-03-29 18:33:28

407

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Radius of convergence of $\sum_{n=0}^{\infty}\frac{x^n}{(\cos^{-1}(\sqrt{n+1}-\sqrt{n}))^n}$

Published on 29 Mar 2026 - 18:33

score 343 · Answer 2 · 2026-03-25 09:40:02

343

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I have found a way of computing Euler's number. Is there any possible intuition of how that might be the case?

Published on 25 Mar 2026 - 9:40

score 37 · Answer 3 · 2026-04-11 00:32:02

37

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Is this statement sufficient?

Published on 11 Apr 2026 - 0:32

score 157 · Answer 4 · 2018-12-29 19:56:31

157

Views

What to use for $\lim_{n\to \infty}\int_{[0,1]}\frac{n\sin{x}}{1+n^2\sqrt{x}}dx$

Published on 29 Dec 2018 - 19:56

score 858 · Answer 5 · 2026-04-11 13:16:42

858

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Suppose that $f_n\to f$ and $g_n\to g$, as $n\to \infty,$ uniformly. Then, $f_n g_n\to fg,$ as $n\to \infty,$ pointwise on $E$.

Published on 11 Apr 2026 - 13:16

score 866 · Answer 6 · 2018-12-30 07:25:39

866

Views

Uncountable Set with Co-countable topology is not a Sequential Space

Published on 30 Dec 2018 - 7:25

score 773 · Answer 7 · 2026-03-26 04:28:56

773

Views

Comparison Test for complex series: logical argument?

Published on 26 Mar 2026 - 4:28

score 195 · Answer 8 · 2026-03-29 16:50:09

195

Views

Different ways of proving that $|\sum^{\infty}_{k=1}(1-\cos(1/k))|\leq 2 $

Published on 29 Mar 2026 - 16:50

score 707 · Answer 9 · 2026-04-11 14:03:53

707

Views

Difference in meaning between converges against and converge to

Published on 11 Apr 2026 - 14:03

score 98 · Answer 10 · 2026-03-30 23:56:48

98

Views

Two similar irrational numbers, Coincidence or Correlation?

Published on 30 Mar 2026 - 23:56

score 88 · Answer 11 · 2026-04-03 00:31:39

88

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If $\sum_{n=1}^{\infty} \sum_{k=1}^{\infty} f_{n}(k) = \infty$ then $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} f_{n}(k) = \infty$.

Published on 03 Apr 2026 - 0:31

score 52 · Answer 12 · 2019-01-01 09:06:31

52

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Check convergence /divergence of a series $\sum_{n=1}^{\infty} (-1)^{n+1}(n)^{\frac{1}{4}}(\frac{1}{\sqrt{4n-1}}- \frac{1}{\sqrt{4n}} )$

Published on 01 Jan 2019 - 9:06

score 35 · Answer 13 · 2019-01-01 13:01:20

35

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Radius of convergence greater than 1 if $f$ is analytic in $\left\{|z| < 1 \right\} \cup{} \left\{1 \right\}$ and $a_n \ge 0$

Published on 01 Jan 2019 - 13:01

score 191 · Answer 14 · 2026-03-28 01:35:17

191

Views

Finding Radius of Convergence of the Power Series

Published on 28 Mar 2026 - 1:35

score 76 · Answer 15 · 2019-01-01 20:29:14

76

Views

Study the convergence of the series $\sum_{n=1}^\infty \left( \sqrt[17]{5+ \frac1n} - \sqrt[17]{5}\right)^{a}q^n$ for $a>0$ and $q\in\mathbb R$

Published on 01 Jan 2019 - 20:29

List Question

Radius of convergence of $\sum_{n=0}^{\infty}\frac{x^n}{(\cos^{-1}(\sqrt{n+1}-\sqrt{n}))^n}$

I have found a way of computing Euler's number. Is there any possible intuition of how that might be the case?

Is this statement sufficient?

What to use for $\lim_{n\to \infty}\int_{[0,1]}\frac{n\sin{x}}{1+n^2\sqrt{x}}dx$

Suppose that $f_n\to f$ and $g_n\to g$, as $n\to \infty,$ uniformly. Then, $f_n g_n\to fg,$ as $n\to \infty,$ pointwise on $E$.

Uncountable Set with Co-countable topology is not a Sequential Space

Comparison Test for complex series: logical argument?

Different ways of proving that $|\sum^{\infty}_{k=1}(1-\cos(1/k))|\leq 2 $

Difference in meaning between converges against and converge to

Two similar irrational numbers, Coincidence or Correlation?

If $\sum_{n=1}^{\infty} \sum_{k=1}^{\infty} f_{n}(k) = \infty$ then $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} f_{n}(k) = \infty$.

Check convergence /divergence of a series $\sum_{n=1}^{\infty} (-1)^{n+1}(n)^{\frac{1}{4}}(\frac{1}{\sqrt{4n-1}}- \frac{1}{\sqrt{4n}} )$

Radius of convergence greater than 1 if $f$ is analytic in $\left\{|z| < 1 \right\} \cup{} \left\{1 \right\}$ and $a_n \ge 0$

Finding Radius of Convergence of the Power Series

Study the convergence of the series $\sum_{n=1}^\infty \left( \sqrt[17]{5+ \frac1n} - \sqrt[17]{5}\right)^{a}q^n$ for $a>0$ and $q\in\mathbb R$

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