| n |
| a1+2a2+3a3+…+nan |
| 2 |
| n+2 |
∴a1+2a2+3a3+…+nan=
| n(n+2) |
| 2 |
∴a1+2a2+3a3+…+（n-1）an-1=
| (n-1)(n+1) |
| 2 |
两式相减，得nan=
| n(n+2)-(n-1)(n+1) |
| 2 |
∴an=
| 2n+1 |
| 2n |
| 1 |
| 2n |
故选：A．
| n |
| a1+2a2+3a3+…+nan |
| 2 |
| n+2 |
| 1 |
| 2n |
| 1 |
| n |
| 1 |
| 2 |
| 1 |
| 2 |
| n |
| a1+2a2+3a3+…+nan |
| 2 |
| n+2 |
| n(n+2) |
| 2 |
| (n-1)(n+1) |
| 2 |
| n(n+2)-(n-1)(n+1) |
| 2 |
| 2n+1 |
| 2n |
| 1 |
| 2n |