交項級数(alternating series)

確認問題

1.
次の級数は条件収束か絶対収束か判定しよう. (a) $\displaystyle{1 + (-1) + 1 + \cdots + (-1)^{n} + \cdots}$ (b) $\displaystyle{\frac{1}{2} - \frac{2}{3} + \frac{3}{4} - \frac{4}{5} + \cdots + (-1)^{n}\frac{n}{n+1} + \cdots }$ (c) $\displaystyle{\frac{1}{2} - \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{...
...rac{1}{7} + \cdots + \frac{1}{3n+2} - \frac{1}{3n+3} - \frac{1}{3n+4} + \cdots}$
演習問題

1.
次の級数は条件収束か絶対収束か判定しよう.

(a) $\displaystyle{\sum (-1)^{n}\frac{\log{n}}{n}}$ (b) $\displaystyle{\sum (-1)^{n} \frac{n}{3^{n}}}$ (c) $\displaystyle{\sum (\frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n+1}})}$

(d) $\displaystyle{\sum \frac{(-1)^{n-1}}{2n - 1}}$ (e) $\displaystyle{\sum \frac{(-1)^{n}}{n\log{n}}}$ (f) $\displaystyle{\sum \frac{\cos{n \pi}}{\sqrt{n^3 + n}}}$