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
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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