List questions from convergence-divergence

Published on 11 Apr 2026 - 3:43

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Example of a Non-negative Martingale Satisfying Certain Conditions

Published on 13 Apr 2026 - 13:14

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Is $x_n = \sum_{i \in \mathbb{N}, \frac{m+ik-1}{n-1} \in [0,1]} |f(\frac{m+ik-1}{n-1})- f(\frac{m+(i-1)k-1}{n-1})|$ convergent when $f\in C\cap BV$?

Published on 15 Mar 2019 - 12:44

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Does the series $\sum_{n=2}^\infty \frac{(-1)^n}{n \ln(n)}$ converge or diverge?

Published on 14 Apr 2026 - 0:08

114

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Convergence in probability of non-negative random variable and expectation

Published on 11 Apr 2026 - 11:33

88

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Do non-negative submartingales with finite second moment converge almost surely?

Published on 12 Apr 2026 - 10:24

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Why does $\int_0^\infty \cos x^2 dx$ converge?

Published on 16 Mar 2019 - 18:33

84

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Convergence of independent random variables

Published on 12 Apr 2026 - 22:50

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Show that an alternating series diverges for $a=0$

Published on 13 Apr 2026 - 19:37

110

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Hint: Showing $f_{n}(x):=\frac{n\sqrt{x} \sin{(x)}}{1+nx^{2}}$ converges in $L^{p}$ to $x^{-\frac{3}{2}}\sin{(x)}$

Published on 30 Mar 2026 - 8:07

125

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Consistent estimator problem

Published on 11 Apr 2026 - 9:57

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Convergence of $a_n = \frac{1}{n} \cdot \frac{1\cdot3\cdot\ldots\cdot(2n-1)}{2\cdot4\cdot\ldots\cdot(2n)}$

Published on 17 Mar 2019 - 0:28

4.2k

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How to evaluate whether summation of $e^n/(ne^n+1)$ diverges or converges?

Published on 28 Mar 2026 - 4:50

730

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Convergence in Probability with respect to expectation and variance

Published on 12 Apr 2026 - 2:22

21

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Problem with one implication in equivalence

Published on 09 Apr 2026 - 21:35

List Question

Problem with truthfulness of equivalence.

Example of a Non-negative Martingale Satisfying Certain Conditions

Is $x_n = \sum_{i \in \mathbb{N}, \frac{m+ik-1}{n-1} \in [0,1]} |f(\frac{m+ik-1}{n-1})- f(\frac{m+(i-1)k-1}{n-1})|$ convergent when $f\in C\cap BV$?

Does the series $\sum_{n=2}^\infty \frac{(-1)^n}{n \ln(n)}$ converge or diverge?

Convergence in probability of non-negative random variable and expectation

Do non-negative submartingales with finite second moment converge almost surely?

Why does $\int_0^\infty \cos x^2 dx$ converge?

Convergence of independent random variables

Show that an alternating series diverges for $a=0$

Hint: Showing $f_{n}(x):=\frac{n\sqrt{x} \sin{(x)}}{1+nx^{2}}$ converges in $L^{p}$ to $x^{-\frac{3}{2}}\sin{(x)}$

Consistent estimator problem

Convergence of $a_n = \frac{1}{n} \cdot \frac{1\cdot3\cdot\ldots\cdot(2n-1)}{2\cdot4\cdot\ldots\cdot(2n)}$

How to evaluate whether summation of $e^n/(ne^n+1)$ diverges or converges?

Convergence in Probability with respect to expectation and variance

Problem with one implication in equivalence

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