1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72=(1/2+1/6+1/12+1/72)+(1/20+1/30)+(1/42+1/56)=(36+12+6+1)/72+(3+2)/60+(8+6)/336=55/72+1/12+1/24=(55+6+3)/72=64/72=8/9