List questions from convergence-divergence

Published on 29 Mar 2026 - 18:32

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Questions on Showing $X_{n}Y_{n}\xrightarrow{P} XY$

Published on 02 Apr 2026 - 14:37

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Improper integral convergence $I = \int_{0^+}^{1^-}\frac{\log(x)}{1-x}dx$

Published on 28 Mar 2026 - 1:35

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Brezis 4.15, $f_n(x)=ne^{−nx}$

Published on 25 Mar 2026 - 1:31

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D'Alembert criterion

Published on 10 Jan 2019 - 22:18

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If $P(\max_{n \leq i \leq j \leq k \leq m} \min \{|S_i - S_j|, |S_k - S_j|\} \geq \lambda)$ is bounded appropriately, does $\sum \xi_j$ converge a.s.?

Published on 25 Mar 2026 - 1:29

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Show that for $|a|<1$ the series $\sum_{n=1}^{\infty}a^nf_n$ converges in $L_2([-1,1])$.

Published on 28 Mar 2026 - 22:31

140

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If $X_n$ converges in distribution to $X$ and $E[X^2]$ is finite, could we have $E[X_n^2]$ is finite?

Published on 11 Jan 2019 - 5:03

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Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence?

Published on 28 Mar 2026 - 1:35

412

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Proof of divergence of power series in Theorem 3.39, baby Rudin

Published on 29 Mar 2026 - 20:21

70

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Does $2\sum\frac{1}{(2k+1)3^{2k+1}}$ converge to $\ln 2$ linearly?

Published on 25 Mar 2026 - 23:38

37

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Convergence in probability towards a constant

Published on 25 Mar 2026 - 11:09

131

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Uniform convergence for operator of translation

Published on 11 Apr 2026 - 22:12

90

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Limit of the function $\lim_{x\to 0}(\frac{e^{-x}-1}{x})$

Published on 27 Mar 2026 - 8:42

432

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If $T_n\to T$ strongly and $x_n\to x$ weakly, must $T_nx_n\to Tx$ weakly?

Published on 28 Mar 2026 - 4:35

List Question

Excercise 4.3 (3) in Brezis. Convergence in $L_p$

Questions on Showing $X_{n}Y_{n}\xrightarrow{P} XY$

Improper integral convergence $I = \int_{0^+}^{1^-}\frac{\log(x)}{1-x}dx$

Brezis 4.15, $f_n(x)=ne^{−nx}$

D'Alembert criterion

If $P(\max_{n \leq i \leq j \leq k \leq m} \min \{|S_i - S_j|, |S_k - S_j|\} \geq \lambda)$ is bounded appropriately, does $\sum \xi_j$ converge a.s.?

Show that for $|a|<1$ the series $\sum_{n=1}^{\infty}a^nf_n$ converges in $L_2([-1,1])$.

If $X_n$ converges in distribution to $X$ and $E[X^2]$ is finite, could we have $E[X_n^2]$ is finite?

Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence?

Proof of divergence of power series in Theorem 3.39, baby Rudin

Does $2\sum\frac{1}{(2k+1)3^{2k+1}}$ converge to $\ln 2$ linearly?

Convergence in probability towards a constant

Uniform convergence for operator of translation

Limit of the function $\lim_{x\to 0}(\frac{e^{-x}-1}{x})$

If $T_n\to T$ strongly and $x_n\to x$ weakly, must $T_nx_n\to Tx$ weakly?

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