List questions from convergence-divergence

79

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Let ${\{x^k\}}^{\infty}_{k=1}$ $\subset R^n$ be a convergent sequence, prove that there exists $B > 0$ such that $∥x^k∥ ≤ B$ for all $k$.

Published on 06 May 2026 - 8:45

76

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Computing the series$\sum\limits_{k=1}^{\infty}{\frac{3^{k-1}+(2i)^k}{5^k}} $

Published on 05 May 2026 - 15:34

105

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Are given functions regulated?

Published on 07 May 2026 - 0:51

90

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Limit of $f_n(x)=f(x)(1+(sin x)^n)$

Published on 10 May 2026 - 12:34

156

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Convergence of a series involving $\sin(n)^n$

Published on 14 Apr 2026 - 18:13

69

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Convergence of unknown series

Published on 06 May 2026 - 13:47

82

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Counter example for incorrectly formulated series convergence test statements

Published on 06 May 2026 - 10:42

116

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Convergence of $\ln\frac{x}{\ln\frac{x}{\ln x...}}$

Published on 06 May 2026 - 0:24

458

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Help verifying the Lindeberg condition

Published on 01 May 2026 - 12:00

856

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Divergence in the Complex Plane

Published on 05 May 2026 - 9:19

5.1k

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Rate of convergence of Newton's method near a double root.

Published on 10 May 2026 - 13:43

249

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When is the pointwise convergence on $A$ equivalent to the uniform one?

Published on 29 Apr 2026 - 12:43

923

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Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $

Published on 16 Apr 2026 - 13:27

64

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Trying to calculate the series $\sum_{n=0}^{\infty}{{-1}\choose n}z^n$

Published on 05 May 2026 - 15:17

97

Views

For what values of $z$ is $\sum_{n=0}^\infty\frac{z^n}{1+z^{2n}}$ convergent?

Published on 10 May 2026 - 11:42

List Question

Let ${\{x^k\}}^{\infty}_{k=1}$ $\subset R^n$ be a convergent sequence, prove that there exists $B > 0$ such that $∥x^k∥ ≤ B$ for all $k$.

Computing the series$\sum\limits_{k=1}^{\infty}{\frac{3^{k-1}+(2i)^k}{5^k}} $

Are given functions regulated?

Limit of $f_n(x)=f(x)(1+(sin x)^n)$

Convergence of a series involving $\sin(n)^n$

Convergence of unknown series

Counter example for incorrectly formulated series convergence test statements

Convergence of $\ln\frac{x}{\ln\frac{x}{\ln x...}}$

Help verifying the Lindeberg condition

Divergence in the Complex Plane

Rate of convergence of Newton's method near a double root.

When is the pointwise convergence on $A$ equivalent to the uniform one?

Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $

Trying to calculate the series $\sum_{n=0}^{\infty}{{-1}\choose n}z^n$

For what values of $z$ is $\sum_{n=0}^\infty\frac{z^n}{1+z^{2n}}$ convergent?

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