| 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) |
计算：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+2008)(x+2009)．
计算：
+
+
+…+
．
| 1 |
| x(x+1) |
| 1 |
| (x+1)(x+2) |
| 1 |
| (x+2)(x+3) |
| 1 |
| (x+2008)(x+2009) |
数学人气：766 ℃时间：2020-01-27 22:37:59
优质解答
∵
=
-
，
=
-
，
∴
=
-
，
∴原式=
-
+
-
+
-
+…+
-
=
-
=
．
∴
∴原式=
=
=
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