1乘2分之1加2乘3分之1加3乘4分之1加4乘5分之1加省略号加2001乘2002分之1=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......+(1/2001-1/2002)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/2001-1/2002=1-1/2002=2001/2002
1/[x*(x+1)]=1/x-1/(x+1)
所以原式=1-1/2+1/2-1/3+1/3-1/4.....-1/2001+1/2001-
1/2002=1-1/2002=2001/2002
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