| 1/3 - 1/2 | + | 1/4 - 1/3 | + | 1/5 - 1/4 | +```+| 1/2007 -1/2006 | + | 1/2008-1/2007 (解题思路)
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| 1/3 - 1/2 | + | 1/4 - 1/3 | + | 1/5 - 1/4 | +```+| 1/2007 -1/2006 | + | 1/2008-1/2007 (解题思路)
| 1/3 - 1/2 | + | 1/4 - 1/3 | + | 1/5 - 1/4 | +```+| 1/2007 -1/2006 | + | 1/2008-1/2007
(解题思路)
| 1/3 - 1/2 | + | 1/4 - 1/3 | + | 1/5 - 1/4 | +```+| 1/2007 -1/2006 | + | 1/2008-1/2007 (解题思路)
| 1/3 - 1/2 | + | 1/4 - 1/3 | + | 1/5 - 1/4 | +```+| 1/2007 -1/2006 | + | 1/2008-1/2007 | =1/2-1/3+1/3-1/4+...+1/2007-1/2008 =1/2-1/2008 =1003/2008