1/8+1/24+1/48+1/80+1/120
=1/4×(1/2+1/6+1/12+1/20+1/30)
=1/4×(1/1*2+1/2*3+1/3*4+1/4*5+1/5*6)
=1/4×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)
=1/4×(1-1/6)
=1/4×5/6
=5/24