| 1 |
| 2 |
| 1 |
| 4n2−1 |
∴an+1−an＝
| 1 |
| (2n−1)(2n+1) |
| 1 |
| 2 |
| 1 |
| 2n−1 |
| 1 |
| 2n+1 |
∴a2−a1＝
| 1 |
| 2 |
| 1 |
| 3 |
a3−a2＝
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 5 |
…
an−an−1＝
| 1 |
| 2 |
| 1 |
| 2n−3 |
| 1 |
| 2n−1 |
以上n-1个式子相加可得，an−a1＝
| 1 |
| 2 |
| 1 |
| 2n−1 |
| 2n−2 |
| 4n−2 |
∵a1＝
| 1 |
| 2 |
∴an=
| 2n−2 |
| 4n−2 |
| 1 |
| 2 |
| 4n−3 |
| 4n−2 |
故答案为：
| 4n−3 |
| 4n−2 |
| 1 |
| 2 |
| 1 |
| 4n2−1 |
| 1 |
| 2 |
| 1 |
| 4n2−1 |
| 1 |
| (2n−1)(2n+1) |
| 1 |
| 2 |
| 1 |
| 2n−1 |
| 1 |
| 2n+1 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 2 |
| 1 |
| 2n−3 |
| 1 |
| 2n−1 |
| 1 |
| 2 |
| 1 |
| 2n−1 |
| 2n−2 |
| 4n−2 |
| 1 |
| 2 |
| 2n−2 |
| 4n−2 |
| 1 |
| 2 |
| 4n−3 |
| 4n−2 |
| 4n−3 |
| 4n−2 |