| 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)](/uploads/image/z/3968681-41-1.jpg?t=%7C+1%2F3+-+1%2F2+%7C+%2B+%7C+1%2F4+-+1%2F3+%7C+%2B+%7C+1%2F5+-+1%2F4+%7C+%2B%60%60%60%2B%7C+1%2F2007+-1%2F2006+%7C+%2B+%7C+1%2F2008-1%2F2007+%EF%BC%88%E8%A7%A3%E9%A2%98%E6%80%9D%E8%B7%AF%EF%BC%89)
| 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