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Mathematics
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HGF
  • Member for 7 years, 3 months
  • Last seen this week
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26
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About

A poor man who love math

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question
20
Find the limit $\lim\limits_{s\to0^+}\sum_{n=1}^\infty\frac{\sin n}{n^s}$
Mar 19, 2022
question
9
$x_n=f\left(\frac{1}{n^2}\right)+f\left(\frac{2}{n^2}\right)+\cdots+f\left(\frac{n}{n^2}\right)$, $\lim_{n\to\infty}x_n=\dfrac{f'(0)}{2}$
Nov 16, 2021
question
9
$\sum_{n=1}^\infty\ln(1+u_n)$ converges but $\sum_{n=1}^\infty u_n$ diverges
May 12, 2023
question
4
Tauberian Theorem and Prime Number Theorem
Jul 20, 2020
question
4
Let $f(x)\in C^2[0,2]$, prove that there exists a $\xi\in(0,2)$ such that $\int_0^2f(x)dx=2f(1)+\frac{f''(\xi)}{3}$.
Dec 14, 2023
question
3
Is the function $f(x)=\sqrt[x+1]{\Gamma(x+2)}-\sqrt[x]{\Gamma(x+1)}$ decreasing?
Jul 9, 2021
answer
3
Find the limit $\lim\limits_{s\to0^+}\sum_{n=1}^\infty\frac{\sin n}{n^s}$
Mar 20, 2022
question
3
$1^\alpha+2^\alpha+3^\alpha+\cdots+n^\alpha$
May 26
question
2
Let $U$ be a subset of $\mathbb{R}^2\setminus\{0\}$, $i_\ast(\pi_1(U))=0$ or $\mathbb{Z}$
Mar 24, 2020
question
2
Great Picard's Theorem and infinite number of poles
Feb 8, 2021
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5
Inequality of arithmetic, geometric and harmonic means