級数の定義(definition of series)

演習問題

1.: 次の級数の収束，発散を判定しよう．
(a): $\displaystyle{\sum_{n=1}^{\infty}\frac{2^{n}+1}{3^{n}+1}}$
(b): $\displaystyle{\sum_{n=1}^{\infty}\frac{1}{n}(\sqrt{n^2 + 1} + \sqrt{n^2 - 1})}$
(c): $\displaystyle{\sum_{n=1}^{\infty}\cos{\frac{\pi}{n}}}$
2.: 次の級数の和を求めよう．
(a): $\displaystyle{\sum_{n=1}^{\infty}\frac{1}{4n^2 - 1}}$
(b): $\displaystyle{\sum_{n=1}^{\infty}\frac{n}{(n+1)!}}$
(c): $\displaystyle{\sum_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)}}$