| 3n + 5 | ||
an = | ||
| n + 1 |
| 3(n+1)+5 | 3n+8 | |||
an+1= | = | |||
| n+1+1 | n+2 |
| 3n+8 | 3n+5 | (3n+8)(n+1)−(3n+5)(n+2) | ||||
an+1−an= | − | = | ||||
| n+2 | n+1 | (n+2)(n+1) |
| 3n2+11n+8−3n2−11n−10 | ||
= | ||
| (n+2)(n+1) |
| −2 | ||
an+1−an= | ||
| (n+2)(n+1) |
| 3n+5 | 2 | |||
an = | = 3 + | |||
| n+1 | n+1 |
| 2 | 2 | 2 | 2 | |||||
an+1 − an = | − | < | − | = 0 | ||||
| n+2 | n+1 | n+1 | n+1 |