| 1 | 1 | |||
lim (3n + 4n − 12n) = lim 12n( ( | )n + ( | )n −1 )= −∞ | ||
| 4 | 3 |
?
teraz mam przykład z pierwiastkiem
an= √n2 +2n −1 −n i nie wiem jak się zabrać za niego równania sprzężonym ?
| √n2+2n−1−n | ||
limn→∞an= limn→∞√n2+2n−1−n= limn→∞ | = | |
| 1 |
| (√n2+2n−1−n)(√n2+2n−1+n) | ||
= limn→∞ | = | |
| √n2+2n−1+n |
| n2+2n−1−n2 | 2n−1 | |||
= limn→∞ | = limn→∞ | = | ||
| √n2+2n−1+n | √n2+2n−1+n |
| n(2−1n) | ||
= limn→∞ | = | |
| √n2(1+2n−1n2)+n |
| n(2−1n) | ||
= limn→∞ | = | |
| n√1+2n−1n2+n |
| n(2−1n) | ||
= limn→∞ | = | |
| n(√1+2n−1n2+1) |
| 2−1n | 2−0 | 2 | ||||
= limn→∞ | = [ | ]= | = 1. ![]() | |||
| √1+2n−1n2+1 | √1+0−0+1 | 2 |