3/2+7/6+13/12+21/20+...+421/420
=(1+1/2)+(1+1/6)+(1+1/12)+(1+1/20)+...+(1+1/420)
=[1+1/(1*2)]+[1+1/(2*3)]+[1+1/(3*4)]+[1+1/(4*5)]+...+[1+1/(20*21)]
=(1+1-1/2)+(1+1/2-1/3)+(1+1/3-1/4)+(1+1/4-1/5)+...+(1+1/20-1/21)
=1*20+1-1/21
=440/21