| n sin n! | ||
lim n→∞ | ||
| n2 + 2 |
−n≤ sin n! ≤n / : n2 + 2
| −n | n sin n! | n | |||
≤ | ≤ | ||||
| n2 + 2 | n2 + 2 | n2 + 2 |
| −n | ||
lim n→∞ | =0 | |
| n2 + 2 |
| n | ||
lim n→∞ | =0 | |
| n2 + 2 |
| n sin n! | ||
więc na mocy tw o 3 ciągach: lim n→∞ | =0 | |
| n2 + 2 |
| n | ||
|sin(n!)|≤1 , z granica | =0 gdy n→∞ | |
| n2+2 |
| n | ||
zatem granica | sin(n!)=0 gdy n→∞ | |
| n2+1 |