作业帮1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2007+2008)=
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1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2007+2008)=
1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2007+2008)=
1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2007+2008)=
因为1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
.
1/(99*100)=1/99-1/100
1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)
=(1-1/2)+(1/2-1/3)+.+(1/99-1/100)
=1-1/2008
=2007/2008
拆开,1-1/2008=2007/2008