3*1分之1=(1-1/3)/2
4*2分之1=(1/2-1/4)/2
5*3分之1=(1/3-1/5)/2
6*4分之1=(1/4-1/6)/2
.
22*20分之1=(1/20-1/22)/2
所以
3*1分之1 + 4*2分之1 + 5*3分之1+.+22*20分之1
=(1-1/3)/2+(1/2-1/4)/2+(1/3-1/5)/2+(1/4-1/6)/2+.+(1/20-1/22)/2
=(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/20-1/22)/2
=(1+1/2-1/21-1/22)/2
=(325/231)/2
=325/462