1/3-1/2+1/4-1/3+1/5-1/4+…1/2004-1/2003
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![1/3-1/2+1/4-1/3+1/5-1/4+…1/2004-1/2003](/uploads/image/z/2733524-44-4.jpg?t=1%2F3-1%2F2%2B1%2F4-1%2F3%2B1%2F5-1%2F4%2B%E2%80%A61%2F2004-1%2F2003)
1/3-1/2+1/4-1/3+1/5-1/4+…1/2004-1/2003
1/3-1/2+1/4-1/3+1/5-1/4+…1/2004-1/2003
1/3-1/2+1/4-1/3+1/5-1/4+…1/2004-1/2003
隔项相消,1/3-1/2+1/4-1/3+1/5-1/4+…1/2004-1/2003=1/2004-1/2=-1001/2004