| 1 | 1 | ||
= | |||
| n2+6n+8 | (n+2)(n+4) |
| 1 | 1 | (n+4)−(n+2) | 2 | ||||
− | = | = | |||||
| n+2 | n+4 | (n+2)(n+4) | (n+2)(n+4) |
| 1 | 1 | 1 | 1 | ||||
= | ( | − | ) | ||||
| (n+2)(n+4) | 2 | n+2 | n+4 |
| 1 | 1 | 1 | 1 | ||||
+ | + | + .. + | = | ||||
| 3*5 | 4*6 | 5*7 | (n+2)(n+4) |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||
[ | − | + | − | + | − | + ... + | − | ||||||||
| 2 | 3 | 5 | 4 | 6 | 5 | 7 | n+2 |
| 1 | ||
] | ||
| n+4 |
| 1 | 1 | 1 | 1 | 1 | 1 | |||||||
= | [ | − | ] przechodzimy w n→∞ i mamy S = | * | = | |||||||
| 2 | 3 | n+4 | 2 | 3 | 6 |