List questions from summation-by-parts

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If a series converges, does it still converge if each term is multiplied by an increasing function

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challenging sum $\sum_{k=1}^\infty\frac{H_k^{(2)}}{(2k+1)^2}$

Published on 29 Apr 2026 - 23:25

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Prove $\sum_{k=1}^n\frac{\left(H_k^{(p)}\right)^2}{k^p}=\frac13((H_n^{(p)})^3-H_n^{(3p)})+\sum_{k=1}^n\frac{H_k^{(p)}}{k^{2p}}$

Published on 29 Apr 2026 - 23:27

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Finding an upper bound using summation by parts

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a question on Bernoulli function in the book of Tenenbaum

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Summation with fractions, discrete calculus

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Rearrange a Triple Summation with constraints

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Proof of Expected value by Abel's Summation

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Double Summation indexes problem

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Evaluating $\int_0^n \{x^2\}\,\text{d}x$

Published on 01 Apr 2026 - 0:55

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Complex Summation Notation Question

Published on 05 May 2026 - 21:22

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How to show $\sum_{k=1}^\infty\sum_{n=1}^\infty\frac{H_{n-1}}{n^2(n+k)^2}=\sum_{n=1}^\infty\frac{H_{n-1}^{(2)}}{n^3}$ using series manipulation?

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Order of convergence of series

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Integrate ${\sin(x)\cos(x)}$ by parts, by letting ${u=\cos(x),dv=\sin(x)dx}$

Published on 29 Apr 2026 - 23:27

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A rotating polygonal line with increasing side length cannot end up where it started!

If a series converges, does it still converge if each term is multiplied by an increasing function

challenging sum $\sum_{k=1}^\infty\frac{H_k^{(2)}}{(2k+1)^2}$

Prove $\sum_{k=1}^n\frac{\left(H_k^{(p)}\right)^2}{k^p}=\frac13((H_n^{(p)})^3-H_n^{(3p)})+\sum_{k=1}^n\frac{H_k^{(p)}}{k^{2p}}$

Finding an upper bound using summation by parts

a question on Bernoulli function in the book of Tenenbaum

Summation with fractions, discrete calculus

Rearrange a Triple Summation with constraints

Proof of Expected value by Abel's Summation

Double Summation indexes problem

Evaluating $\int_0^n \{x^2\}\,\text{d}x$

Complex Summation Notation Question

How to show $\sum_{k=1}^\infty\sum_{n=1}^\infty\frac{H_{n-1}}{n^2(n+k)^2}=\sum_{n=1}^\infty\frac{H_{n-1}^{(2)}}{n^3}$ using series manipulation?

Order of convergence of series

Integrate ${\sin(x)\cos(x)}$ by parts, by letting ${u=\cos(x),dv=\sin(x)dx}$

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