Question

If $\lim_{n\to\infty} a_n=1$, then does $\lim_{n\to\infty}a_n^{3/2}=1$ also?

score 87 · Answer 1 · 2026-04-15 23:21:49

87

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If $\lim_{n\to\infty} a_n=1$, then does $\lim_{n\to\infty}a_n^{3/2}=1$ also?

Published on 15 Apr 2026 - 23:21

score 132 · Answer 2 · 2026-04-13 14:03:28

132

Views

How to prove the validity of the interchange of summation and integration when the sum doesn't converge absolutely

Published on 13 Apr 2026 - 14:03

score 122 · Answer 3 · 2026-04-15 19:58:49

122

Views

Find the radius of convergence of the power series $\sum_{n=1}^\infty 2^{n^2} \: x^{n!}$

Published on 15 Apr 2026 - 19:58

score 90 · Answer 4 · 2026-04-14 15:55:50

90

Views

Must there exist a number of digits $n$, for which the first $n$ digits of a normal number repeat?

Published on 14 Apr 2026 - 15:55

score 3.9k · Answer 5 · 2026-04-13 11:31:39

3.9k

Views

How to show this sequence is decreasing

Published on 13 Apr 2026 - 11:31

score 87 · Answer 6 · 2026-04-15 09:40:55

87

Views

Proving logarithmic property for series convergence

Published on 15 Apr 2026 - 9:40

score 108 · Answer 7 · 2026-04-17 13:57:37

108

Views

What is the closed form solution for this integral or series?

Published on 17 Apr 2026 - 13:57

score 180 · Answer 8 · 2026-04-14 21:43:55

180

Views

Step in proof of $\sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}$

Published on 14 Apr 2026 - 21:43

score 60 · Answer 9 · 2026-04-16 17:44:39

60

Views

How to find the limit of this series

Published on 16 Apr 2026 - 17:44

score 151 · Answer 10 · 2026-04-16 13:35:55

151

Views

$\lim_{n\rightarrow\infty}\sum_{r=0}^{n-1}\sum_{k=0}^{n-r}(-1)^k\frac{2n+3}{k!(2n+3-k)!} (1+n-r-k)^{2n+1}=0$

Published on 16 Apr 2026 - 13:35

score 1.6k · Answer 11 · 2026-04-24 11:23:11

1.6k

Views

Is there a function that gives unique values when a unique sequence of numbers is given as input?

Published on 24 Apr 2026 - 11:23

score 75 · Answer 12 · 2026-04-11 01:09:53

75

Views

Does the following $\sin$-series converges?

Published on 11 Apr 2026 - 1:09

score 302 · Answer 13 · 2026-04-15 05:05:07

302

Views

Show that the series $x_n = \sum_{k=1}^{n} (-1)^{k+1}/k$ is Cauchy

Published on 15 Apr 2026 - 5:05

score 69 · Answer 14 · 2026-04-16 01:26:58

69

Views

Finding a sequence $a_n$ that diverges such that $\|a_n\|$ converges (in $\mathbb{R}$)

Published on 16 Apr 2026 - 1:26

score 255 · Answer 15 · 2026-04-14 23:31:54

255

Views

Convergent series after rearrangement becomes divergent

Published on 14 Apr 2026 - 23:31

List Question

If $\lim_{n\to\infty} a_n=1$, then does $\lim_{n\to\infty}a_n^{3/2}=1$ also?

How to prove the validity of the interchange of summation and integration when the sum doesn't converge absolutely

Find the radius of convergence of the power series $\sum_{n=1}^\infty 2^{n^2} \: x^{n!}$

Must there exist a number of digits $n$, for which the first $n$ digits of a normal number repeat?

How to show this sequence is decreasing

Proving logarithmic property for series convergence

What is the closed form solution for this integral or series?

Step in proof of $\sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}$

How to find the limit of this series

$\lim_{n\rightarrow\infty}\sum_{r=0}^{n-1}\sum_{k=0}^{n-r}(-1)^k\frac{2n+3}{k!(2n+3-k)!} (1+n-r-k)^{2n+1}=0$

Is there a function that gives unique values when a unique sequence of numbers is given as input?

Does the following $\sin$-series converges?

Show that the series $x_n = \sum_{k=1}^{n} (-1)^{k+1}/k$ is Cauchy

Finding a sequence $a_n$ that diverges such that $\|a_n\|$ converges (in $\mathbb{R}$)

Convergent series after rearrangement becomes divergent

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