| 3n * n! | ||
∑ | ||
| (2n)! |
| 3n * n! | ||
an = | ||
| (2n)! |
| 3n+1(n+1)! | 3 * 3n * n!(n + 1) | |||
an + 1 = | = | |||
| (2n + 2)! | (2n)! * (2n + 1)(2n + 2) |
| an+1 | 3 * 3n * n!(n + 1) | (2n)! | |||
= | * | = | |||
| an | (2n)! * (2n + 1)(2n + 2) | 3n * n! |
| 3 (n + 1) | ||
= | → 0 < 1 zatem szereg zbieżny | |
| (2n + 1)(2n + 2) |
| n − 3 | ||
∑ a−n * ( | )n2 | |
| n |
| n − 3 | ||
an = a−n * ( | )n2 | |
| n |
| n − 3 | 3 | 1 | ||||
n√an = a−1 ( | )n = a−1 * (1 − | )n → a−1 * e−3 = | ||||
| n | n | ae3 |
| 1 | ||
Jeśli ae3 > 1 ⇔ a > | to szereg zbieżny | |
| e3 |
| 1 | 1 | |||
Jeśli ae3 < 1 ⇔ a < | ⇒ a ∊ (0, | ) to szereg rozbieżny | ||
| e3 | e3 |
| 1 | ||
Dla a = | trzeba pokombinować jakimś kryterium. | |
| e3 |
| 1 | ||
Ale raczej zbieżny dla a = | . Można się bawić w ograniczenia | |
| e3 |