Ograniczenie ciągu
Klaudia: Czy podany ciąg jest ograniczony z góy
an= 1/(41+ 1) + 1/(42 + 2) + ... 1/(4n + n)
7 gru 20:42
Gray: | | 1 | | 1 | | 1 | | 1 | |
an≤ |
| + |
| + |
| + ... + |
| ≤ |
| | 4 | | 42 | | 43 | | 4n | |
| | 1 | | 1 | | 1 | | 1 | | 1/4 | | 1 | |
≤ |
| + |
| + |
| + ... + |
| + .... = |
| = |
| , więc jest |
| | 4 | | 42 | | 43 | | 4n | | 1−1/4 | | 3 | |
ograniczony.
7 gru 20:46