List questions from sequences-and-series

Published on 11 Apr 2026 - 15:46

20

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To prove a sequence is convergent

Published on 06 Apr 2026 - 18:58

76

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Given a convergence series $\sum 3^na_n$. Prove/disprove: The series $\sum (-2)^na_n$ converges.

Published on 31 Jan 2018 - 8:46

50

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Value of $S_{10}+I_{10}$

Published on 31 Jan 2018 - 8:48

78

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p-adic series $\sum n!$

Published on 11 Apr 2026 - 23:49

236

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Counterexample of Gnedenko in probability theory (about an integral of $f(x) = \frac{1-\cos x}{\pi x^2}$ and a series)

Published on 25 Mar 2026 - 3:04

2.1k

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Is the sum of the series $\sum \frac{\sin nx^2}{1 + n^3}$ continuously differentiable?

Published on 31 Jan 2018 - 12:10

121

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Determining whether sequence $a_n=\sum_{k=1}^n\frac n{n^2+k}$ is convergent or not.

Published on 08 Apr 2026 - 23:00

251

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Divergence of a Series $\sum_{n=1}^\infty (\frac{1}{n!})(\frac{n}{e})^n$

Published on 09 Apr 2026 - 2:45

1.1k

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Double summation involving factorials

Published on 11 Apr 2026 - 13:12

1.8k

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What is the closed form of the sequence : $ a_{n+2} = 2a_{n+1}-a_n+2^n+2 $

Published on 09 Apr 2026 - 4:50

207

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Find the closed form of $u_{n+1}=a_nu_n+b_n$

Published on 09 Apr 2026 - 3:14

74

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limitof the series $\sum_{k=2}^{\infty}{\frac{2^{k+1}+3^k}{4^{k-1}}}$

Published on 09 Apr 2026 - 21:15

49

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Does the function have a factor as a power of 2?

Published on 10 Apr 2026 - 19:56

2.9k

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Using sequences to prove a limit doesn't exist?

Published on 25 Mar 2026 - 11:52

List Question

Can a subsequence repeat a term finitely many times?

To prove a sequence is convergent

Given a convergence series $\sum 3^na_n$. Prove/disprove: The series $\sum (-2)^na_n$ converges.

Value of $S_{10}+I_{10}$

p-adic series $\sum n!$

Counterexample of Gnedenko in probability theory (about an integral of $f(x) = \frac{1-\cos x}{\pi x^2}$ and a series)

Is the sum of the series $\sum \frac{\sin nx^2}{1 + n^3}$ continuously differentiable?

Determining whether sequence $a_n=\sum_{k=1}^n\frac n{n^2+k}$ is convergent or not.

Divergence of a Series $\sum_{n=1}^\infty (\frac{1}{n!})(\frac{n}{e})^n$

Double summation involving factorials

What is the closed form of the sequence : $ a_{n+2} = 2a_{n+1}-a_n+2^n+2 $

Find the closed form of $u_{n+1}=a_nu_n+b_n$

limitof the series $\sum_{k=2}^{\infty}{\frac{2^{k+1}+3^k}{4^{k-1}}}$

Does the function have a factor as a power of 2?

Using sequences to prove a limit doesn't exist?

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