31. 求下列级数的和
Posted by haifeng on 2019-12-17 13:38:35 last update 2023-05-01 09:53:19 | Answers (3) | 收藏
(1)
\[
\sum_{n=1}^{+\infty}\frac{1}{n(2n-1)}
\]
(2)
\[
\sum_{n=1}^{+\infty}(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n})
\]
(3)
\[
\sum_{n=1}^{+\infty}\frac{1}{n(n+3)}
\]
(4)
\[
\sum_{n=1}^{+\infty}\frac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}
\]
(5)
\[
\sum_{n=1}^{+\infty}\frac{(-1)^{n-1}}{n}
\]
(6)
\[
\sum_{n=1}^{+\infty}\frac{1}{n(n+1)(n+2)}
\]