| (n!)2 | ||
∑ | ||
| (2n)! |
| ( n ! )2 | ||
an = | ||
| ( 2 n) ! |
| ( n + 1) !)2 | ( n ! *(n +1))2 | |||
an+1 = | = | = | ||
| ( 2*( n + 1)) ! | (2n + 2) ! |
| ( n ! *( n + 1))2 | ||
= | ||
| (2n) ! *( 2n +1)*( 2n + 2) |
| an +1 | n2 + 2n + 1 | ||
= | = | ||
| an | 4 n2 + 6n + 2 |
| 1+2n +1n2 | ||
= | ||
| 4 + 6n + 2n2 |
| an +1 | 1 | |||
lim | = | < 1 | ||
| an | 4 |
| (n ! )2 | ||
Szereg ∑ | jest zbieżny na mocy kryterium d'Alemberta. | |
| (2n) ! |