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