| 1 | 1 | 1 | 1 | |||||
lim n→∞ (1− | )(1− | )(1− | )...(1− | )
| ||||
| 22 | 32 | 42 | n2 |
| 1 | ||
Wychodzi z tego | ? | |
| 2 |
| 1 | ||
No mi też wyszło | ||
| 2 |
| 1 | 1 | 1 | 1 | 1 | 1 | |||||||
(1 − | )(1 + | )(1 − | )(1 + | ) * ... (1 − | )(1 + | ) | ||||||
| 2 | 2 | 3 | 3 | n | n |
| 1 | 3 | 2 | 4 | n − 2 | n | n − 1 | n + 1 | ||||||||
* | * | * | * ... * | * | * | * | = | ||||||||
| 2 | 2 | 3 | 3 | n − 1 | n −1 | n | n |
| 1 | n + 1 | n + 1 | |||
* | = | ||||
| 2 | n | 2n |
| n + 1 | 1 | |||
limn−>∞ | = | |||
| 2n | 2 |
| 1 | ||
Tak, ma wyjść | | |
| 2 |