| 1 | 1 | 3 | |||
− | = | ||||
| 3n−1 | 3n+2 | (3n−1)(3n+2) |
| 1 | 1 | 3 | ||||
Inaczej. Zauważ, że | − | = | lub równoważnie: | |||
| 3n−1 | 3n+2 | (3n−1)(3n+2) |
| 1 | 1 | 1 | 1 | ||||
= | ( | − | ). | ||||
| (3n−1)(3n+2) | 3 | 3n−1 | 3n+2 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||||||
an = | ( | − | + | − | + | − | + ...+ | − | ||||||||
| 3 | 2 | 5 | 5 | 8 | 8 | 11 | 3n−1 |
| 1 | ||
) = wszystko się odejmie za wyjątkiem dwóch składników = | ||
| 3n+2 |
| 1 | 1 | 1 | n | |||||
= | ( | − | ) = | |||||
| 3 | 2 | 3n+2 | 6n+4 |