1+ (1+2)分之1+ (1+2+3)分之1+ (1+2+3+4)分之1+.(1+2+3+...100)分之1
=1+2/(1+2)*2+2/(1+3)*3+.2/(1+100)*100
=1+2(1/2-1/3+1/3-1/4+.+1/100-1/101)
=1+2(1/2-1/101)
=1+1-2/101
=200/101