交項級数(alternating series)

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): $\displaystyle{\sum \frac{\cos{n \pi}}{\sqrt{n^3 + n}}}$