(a) \(\displaystyle{\sum_{n=1}^{\infty}\frac{1}{n^4}}\) |
(d) \(\displaystyle{1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\cdots}\) |
(b) \(\displaystyle{\sum_{n=1}^{\infty}\frac{2}{\sqrt[3]{n^2}}}\) |
(e) \(\displaystyle{1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\frac{1}{\sqrt{5}}+\cdots}\) |
(c) \(\displaystyle{\sum_{n=1}^{\infty}\frac{1}{n^{\sqrt{3}}}}\) |
(f) \(\displaystyle{\sum_{n=1}^{\infty}\frac{1}{\sqrt[\pi]{n^4}}}\) |
(a) \(\displaystyle{ \sum_{n=1}^{\infty} \frac{1}{1+n^2}}\) solution |
(b) \(\displaystyle{\sum_{n=1}^{\infty} \frac{\sqrt[3]{n}+2}{n^2}}\) solution 1 solution 2 |
(c) \( \displaystyle {\sum_{n=1}^{\infty} \frac{n}{n^2+4}}\) solution |
(d) \(\displaystyle{\sum_{n=2}^{\infty} \frac{\ln n}{n}}\) solution |
(e) \(\displaystyle{\sum_{n=2}^{\infty} \frac{1}{n\ln n}}\) solution |
(f) \(\displaystyle{\sum_{n=1}^{\infty} n^2 e^{-n^3}}\) solution |
(g) \(\displaystyle{\sum_{n=2}^{\infty} \frac{e^{1/n}}{n^2}}\) solution |
(h) \(\displaystyle{\sum_{n=3}^{\infty} \frac{n^2}{e^n}}\) solution |