| 1 | 1 | 1 | ||||
hej pomoże ktoś przy obliczeniu takiej sumy: | + | + | ||||
| 1*2 | 2*3 | 3*4 |
| 1 | ||
+...+ | =  | |
| 199*200 |
| 1 | 1 | 1 | n | ||||
+ | + ... + | = | dla n∊N. | ||||
| 1*2 | 2*3 | n(n+1) | n+1 |
| 1 | 1 | 1 | |||
= | − | ||||
| 1*2 | 1 | 2 |
| 1 | 1 | 1 | |||
= | − | ||||
| 2*3 | 2 | 3 |
| 1 | 1 | 1 | |||
= | − | stąd | |||
| 199*200 | 199 | 200 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||
− | + | − | +.........+ | − | + | − | =,... | ||||||||
| 1 | 2 | 2 | 3 | 198 | 199 | 199 | 200 |