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HGF

Member for 7 years, 3 months
Last seen this week

Summary

Reputation

935

935
493
51

2021
2022
2023
2024

Top tag

analysis

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1,000 Rep.

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6

14

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Caucus

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~5k

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helpful flags

439

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Questions

View all 26 questions

20

Find the limit $\lim\limits_{s\to0^+}\sum_{n=1}^\infty\frac{\sin n}{n^s}$

Mar 19, 2022

9

$\sum_{n=1}^\infty\ln(1+u_n)$ converges but $\sum_{n=1}^\infty u_n$ diverges

May 12, 2023

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

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

4

Tauberian Theorem and Prime Number Theorem

Jul 20, 2020

Answers

View all 10 answers

3

Find the limit $\lim\limits_{s\to0^+}\sum_{n=1}^\infty\frac{\sin n}{n^s}$

Mar 20, 2022

2

Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$

Jun 11, 2022

1

On the conditions of the Implicit Function Theorem

Feb 23, 2023

1

$1^\alpha+2^\alpha+3^\alpha+\cdots+n^\alpha$

May 26

0

Proving $\left[a_1,\frac{b_1+\sqrt\Delta}2\right]\cdot\left[a_2,\frac{b_2+\sqrt\Delta}2\right]=\left[a_1a_2,\frac{b+\sqrt\Delta}2\right]$

Sep 4

Tags

View all 44 tags

analysis

3

Score

7

posts

calculus

3

Score

5

posts

dirichlet-series

3

Score

3

posts

tauberian-theory

3

Score

2

posts

wieners-tauberian-theorem

3

Score

2

posts

Reputation

+10

Genus of binary quadratic forms

+10

Proving $\left[a_1,\frac{b_1+\sqrt\Delta}2\right]\cdot\left[a_2,\frac{b_2+\sqrt\Delta}2\right]=\left[a_1a_2,\frac{b+\sqrt\Delta}2\right]$

+10

$1^\alpha+2^\alpha+3^\alpha+\cdots+n^\alpha$

+10

$1^\alpha+2^\alpha+3^\alpha+\cdots+n^\alpha$

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Mar 17, 2023
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May 12, 2023

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Apr 17, 2022
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Apr 26, 2021

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343

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