注意到1/1x2=1-1/2
1/2x3=1/2-1/3
1/3x4=1/3-1/4
.
故原式=1-1/2+1/2-1/3+1/3-1/4+1/4.+1/2007-1/2008=1-1/2008
=2007/2008
计算：1/1x2+1/2x3+1/3x4+……+1/2007x2008
8个回答
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