| 2n+1 | ||
an= | ||
| 3n+2 |
| 2(n+1)+1 | 2n+3 | |||
an+1= | = | |||
| 3(n+1)+2 | 3n+5 |
| 2n+3 | 2n+1 | (2n+3)(3n+2)−(2n+1)(3n+5) | ||||
an+1−an= | − | = | = | |||
| 3n+5 | 3n+2 | (3n+5)(3n+2) |
| 6n2+13n+6−6n2−13n−5 | 1 | |||
= | = | |||
| (3n+5)(3n+2) | (3n+5)(3n+2) |
| 3 | ||
ciąg ograniczony z góry przez liczbę: | ||
| 5 |
| 2n+1 | 3n | ||
< | = 1 dla każdego n | ||
| 3n+2 | 3n |
| 2 | ||
to wystarczy, bo nie kazano znaleźć kresu górnego (jest równy | ) | |
| 3 |