List questions from convergence-divergence

Published on 06 Jun 2018 - 10:17

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Convergence of an improper integral.

Published on 28 Mar 2026 - 1:46

1.2k

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When does mean convergence implies almost sure convergence?

Published on 06 Jun 2018 - 15:11

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Square integrable functions and integral convergence

Published on 28 Mar 2026 - 1:47

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If $\sum_{i=1}^na_i /n \to 1$, then $\sum_{i=1}^n a_iX_i /n \to 1$ holds where $X_n$ iid RVs, $EX_1=1$, and $(a_n)$ is a bdd real seq.

Published on 06 Jun 2018 - 17:00

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Let $f : [0,1] \to [0,1]$ continuous and $(u_n)$ s.t. $\forall n, u_{n+1}=f(u_n)$. Show that $(u_n)$ converges $\iff u_{n+1} - u_n \to 0$

Published on 06 Jun 2018 - 18:04

101

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Analyze if the serie is convergent or divergent $\sum_{n=1}^{\infty}\frac{\ln n}{1+n^2}$

Published on 06 Jun 2018 - 21:27

412

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$\sum_{n=1}^{\infty}\frac{4n^2+26n+34}{n^4+10n^3+35n^2+50n+24}$ convergent?

Published on 06 Jun 2018 - 22:00

54

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convergence of random variable with parameter

Published on 07 Jun 2018 - 16:15

242

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What exactly is the weak* convergence in $L^2$ and $L^\infty$?

Published on 07 Jun 2018 - 16:24

181

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Exponential convergence of Taylor series.

Published on 27 Mar 2026 - 8:41

98

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how to prove the following improper integral is diverging $\int_{\pi/2}^{\infty}\left |\frac{\cos(x)}{x+\sin(x)} \right | dx $

Published on 28 Mar 2026 - 1:48

126

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How to prove that an alternate sum is positive? $S(p,n)=\sum _{k=0}^{n+3} (-1)^k \binom{n+2 p+4-k}{2 p+1} \binom{2 n+2 p+7}{k} (n+p+3-k)^{2 n+4}$

Published on 26 Mar 2026 - 20:41

735

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Splitting up an infinite sum

Published on 25 Mar 2026 - 21:45

1.3k

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Convergence criteria for real Riemann zeta function

Published on 27 Mar 2026 - 20:27

List Question

Convergence of a recursive sequence $u_n$

Convergence of an improper integral.

When does mean convergence implies almost sure convergence?

Square integrable functions and integral convergence

If $\sum_{i=1}^na_i /n \to 1$, then $\sum_{i=1}^n a_iX_i /n \to 1$ holds where $X_n$ iid RVs, $EX_1=1$, and $(a_n)$ is a bdd real seq.

Let $f : [0,1] \to [0,1]$ continuous and $(u_n)$ s.t. $\forall n, u_{n+1}=f(u_n)$. Show that $(u_n)$ converges $\iff u_{n+1} - u_n \to 0$

Analyze if the serie is convergent or divergent $\sum_{n=1}^{\infty}\frac{\ln n}{1+n^2}$

$\sum_{n=1}^{\infty}\frac{4n^2+26n+34}{n^4+10n^3+35n^2+50n+24}$ convergent?

convergence of random variable with parameter

What exactly is the weak* convergence in $L^2$ and $L^\infty$?

Exponential convergence of Taylor series.

how to prove the following improper integral is diverging $\int_{\pi/2}^{\infty}\left |\frac{\cos(x)}{x+\sin(x)} \right | dx $

How to prove that an alternate sum is positive? $S(p,n)=\sum _{k=0}^{n+3} (-1)^k \binom{n+2 p+4-k}{2 p+1} \binom{2 n+2 p+7}{k} (n+p+3-k)^{2 n+4}$

Splitting up an infinite sum

Convergence criteria for real Riemann zeta function

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