| 1 |
| x(x+1) |
| 1 |
| x |
| 1 |
| x+1 |
| 1 |
| (x+1)(x+2) |
| 1 |
| x+1 |
| 1 |
| x+2 |
∴
| 1 |
| (x+n)(x+n+1) |
| 1 |
| x+n |
| 1 |
| x+n+1 |
∴原式=
| 1 |
| x |
| 1 |
| x+1 |
| 1 |
| x+1 |
| 1 |
| x+2 |
| 1 |
| x+2 |
| 1 |
| x+3 |
| 1 |
| x+2008 |
| 1 |
| x+2009 |
=
| 1 |
| x |
| 1 |
| x+2009 |
=
| 2009 |
| x(x+2009) |
| 1 |
| x(x+1) |
| 1 |
| (x+1)(x+2) |
| 1 |
| (x+2)(x+3) |
| 1 |
| (x+2008)(x+2009) |
| 1 |
| x(x+1) |
| 1 |
| x |
| 1 |
| x+1 |
| 1 |
| (x+1)(x+2) |
| 1 |
| x+1 |
| 1 |
| x+2 |
| 1 |
| (x+n)(x+n+1) |
| 1 |
| x+n |
| 1 |
| x+n+1 |
| 1 |
| x |
| 1 |
| x+1 |
| 1 |
| x+1 |
| 1 |
| x+2 |
| 1 |
| x+2 |
| 1 |
| x+3 |
| 1 |
| x+2008 |
| 1 |
| x+2009 |
| 1 |
| x |
| 1 |
| x+2009 |
| 2009 |
| x(x+2009) |