1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(20*21*22)
=1/2(1/1*2-1/2*3+1/2*3-1/3*4+……+1/20*21-1/21*22)
=1/2*(1/1*2-1/21*22)
=115/462