1/(1*2)+1/(2*3)+1/(3*4)+L+1/(100*101)=
问题描述：
1/(1*2)+1/(2*3)+1/(3*4)+L+1/(100*101)=
答
解
1/(1*2)+1/(2*3)+……+1/(100*101)
=(1-1/2)+(1/2-1/3)+……+(1/100-1/101)
=1-1/2+1/2-1/3+1/3-……-1/100+1/100-1/101
=1-1/101
=100/101