| 1 |
| 5 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 2×2−1 |
| 1 |
| 2×2+1 |
| 1 |
| 15 |
a3=
| 1 |
| 2×3−1 |
| 1 |
| 2×3+1 |
| 1 |
| 35 |
（2）观察（1）的规律可得：a2008=
| 1 |
| 4015 |
| 1 |
| 4017 |
| 1 |
| 16128255 |
（3）找出一般形式为：an=
| 1 |
| 2 |
| 1 |
| 2n−1 |
| 1 |
| 2n+1 |
∴a1+a2+a3+a2008=
| 1 |
| 2 |
| 1 |
| 1 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 4017 |
| 1 |
| 2 |
| 4016 |
| 4017 |
| 2008 |
| 4017 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 2×2−1 |
| 1 |
| 2×2+1 |
| 1 |
| 15 |
| 1 |
| 2×3−1 |
| 1 |
| 2×3+1 |
| 1 |
| 35 |
| 1 |
| 4015 |
| 1 |
| 4017 |
| 1 |
| 16128255 |
| 1 |
| 2 |
| 1 |
| 2n−1 |
| 1 |
| 2n+1 |
| 1 |
| 2 |
| 1 |
| 1 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 4017 |
| 1 |
| 2 |
| 4016 |
| 4017 |
| 2008 |
| 4017 |