| 1 | 1 | 1 | 1 | |||||
lim ( | + | + | + ... + | ) | ||||
| 1*2 | 2*3 | 3*4 | (n−1)n |
| 1 | 1 | 1 | |||
= | − | ||||
| 1*2 | 1 | 2 |
| 1 | 1 | 1 | |||
= | − | ||||
| 2*3 | 2 | 3 |
| 1 | 1 | 1 | |||
= | − | ||||
| 3*4 | 3 | 4 |
| 1 | 1 | 1 | |||
= | − | ||||
| (n−1)*n | n−1 | n |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||||||
( | − | ) + ( | − | ) + ( | − | ) + ... + ( | − | )= | ||||||||
| 1 | 2 | 2 | 3 | 3 | 4 | n−1 | n |
| 1 | 1 | |||
= | − | |||
| 1 | n |
| 1 | 1 | |||
lim ( | − | ) = 1 − 0 = 1 | ||
| 1 | n |