| 1 | ||
∑n=0∞xn = | ||
| 1−x |
| d | d | 1 | |||
(∑n=0∞xn) = | ( | ) | |||
| dx | dx | 1−x |
| 1 | ||
∑n=0∞nxn−1 = − | (−1) | |
| (1−x)2 |
| 1 | ||
∑n=1∞nxn−1 = | ||
| (1−x)2 |
| 1 | ||
∑n=0∞(n+1)xn = | ||
| (1−x)2 |
| d | d | 1 | |||
(∑n=0∞(n+1)xn)= | ( | ) | |||
| dx | dx | (1−x)2 |
| −2 | ||
∑n=0∞n(n+1)xn−1 = | (−1) | |
| (1−x)3 |
| 2 | ||
∑n=1∞n(n+1)xn−1 = | ||
| (1−x)3 |
| 2 | ||
∑n=0∞(n+1)(n+2)xn = | ||
| (1−x)3 |