1/3=1/(1*3)=1/2*(1-1/3)
1/8=1/(2*4)=1/2*(1/2-1/4)
1/15=1/(3*5)=1/2*(1/3-1/5)
1/24=1/(4*6)=1/2*(1/4-1/6)
.
1/323=1/(17*19)=1/2*(1/17-1/19)
1/360=1/(18*20)=1/2*(1/18-1/20)
1/3+1/8+1/15+1/24+...+1/360
=1/2*[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/17-1/19)+(1/18-1/20)]
=1/2*(1+1/2-1/3+1/3-1/4+...-1/17+1/17-1/18+1/18-1/19-1/20)
=1/2*(1+1/2-1/19-1/20)
=1/2*531/380
=531/760