Introduction
This is an analysis problem from 2022~2023 boling class mathematical-analysis-III mid-term examination paper. This post will show you the problem and its connecting problem from Mathematical-analysis-III of Nankai University Exercise 14(B)-13.
Problem from Exercise Paper
Problem
设 $\alpha\gt0$，讨论级数
\[\displaystyle\sum_{n=1}^{\infty}\frac{\cos\sqrt{n}}{n^{\alpha}}\]的收敛性(若收敛，精确到条件收敛和绝对收敛)
Problem from Textbook
For the more information about the following problem, you can refer to the book Mathematical-analysis-III of Nankai University Exercise 14(B)-13.
Problem
设$\alpha\in(0,1)$，$p>max\lbrace\alpha,1-\alpha\rbrace$，则
\[\displaystyle\sum_{n=1}^{\infty}\frac{\sin n^{\alpha}}{n^p}\]收敛.
Solution for PDF
Click Here and get the solution about these two similar series problems.
Remark
If you have any questions or need further assistance, feel free to ask! Here is my email: nkusherr1 at gmail.com
