1+1/3+1/6+1/10+1/15+…+1/5050
=2/1*2+2/2*3+2*/3*4+2/4*5+2/5*6+…+2/100*101
=2*(1-1/2+1/2-1/3+1/3-1/4+…+1/100-1/101)
=2*(1-1/101)
=200/101