List questions from convergence-divergence

Published on 11 Apr 2026 - 3:35

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Does convergence by the ratio test for sequences implies that the sequence is monotonic?

Published on 25 Mar 2026 - 15:40

634

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Show that there exists no sequence of complex polynomials which converges uniformly to $\frac{1}{z^2}$ on the annulus $1<|z|<2$.

Published on 29 Mar 2026 - 18:36

32

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Uniform convergence of $f_n$ implies convergence in $\mathcal{L}^1([0,1])$

Published on 28 Mar 2026 - 16:17

56

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Convergence of a special sequence.

Published on 13 Jan 2019 - 19:38

76

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Prove convergence of $\sum_{n=2}^\infty \frac{\ln^5{(2n^7 + 13)} + 10\sin{n}}{n \ln^6{(n^{7/8} + \sqrt{n} - 1)} \cdot \ln( \ln (n + (-1)^n))}$

Published on 14 Jan 2019 - 0:26

222

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Vitali's Convergence Theorem but one hypothesis changes

Published on 10 Apr 2026 - 16:51

46

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Show convergence of a serie with unknown exponent

Published on 14 Jan 2019 - 11:44

199

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Weak Star Convergence of $u_n=\sin(\frac{nx}{n+1})(1+\exp{(-n|y|)})$

Published on 09 Apr 2026 - 2:01

110

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Convergence of $L^2$ functions with conditions on their Fourier transforms

Published on 28 Mar 2026 - 6:00

70

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For which positive real numbers $a$ does $\sum_{n=1}^\infty a^{\log n}$ converge?

Published on 14 Jan 2019 - 22:52

107

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Expand $X(z) = \frac{1}{1+az}$ into a causal sequence

Published on 25 Mar 2026 - 22:03

336

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if {an} is a negative decreasing sequence, can it be convergent?

Published on 12 Apr 2026 - 0:36

80

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Convergence in $C([0,T_0],L^2)$ and uniform boundedness in $C([0,T_0],H^2)$ gives convergence in $C([0,T_0],H^1)$.

Published on 29 Mar 2026 - 8:45

124

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Testing series for convergence/divergence

Published on 11 Apr 2026 - 23:42

List Question

Convergence in measure and almost everywhere proof

Does convergence by the ratio test for sequences implies that the sequence is monotonic?

Show that there exists no sequence of complex polynomials which converges uniformly to $\frac{1}{z^2}$ on the annulus $1<|z|<2$.

Uniform convergence of $f_n$ implies convergence in $\mathcal{L}^1([0,1])$

Convergence of a special sequence.

Prove convergence of $\sum_{n=2}^\infty \frac{\ln^5{(2n^7 + 13)} + 10\sin{n}}{n \ln^6{(n^{7/8} + \sqrt{n} - 1)} \cdot \ln( \ln (n + (-1)^n))}$

Vitali's Convergence Theorem but one hypothesis changes

Show convergence of a serie with unknown exponent

Weak Star Convergence of $u_n=\sin(\frac{nx}{n+1})(1+\exp{(-n|y|)})$

Convergence of $L^2$ functions with conditions on their Fourier transforms

For which positive real numbers $a$ does $\sum_{n=1}^\infty a^{\log n}$ converge?

Expand $X(z) = \frac{1}{1+az}$ into a causal sequence

if {an} is a negative decreasing sequence, can it be convergent?

Convergence in $C([0,T_0],L^2)$ and uniform boundedness in $C([0,T_0],H^2)$ gives convergence in $C([0,T_0],H^1)$.

Testing series for convergence/divergence

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