1/2+1/6+1/30+1/42+1/56+1/72
=1/(1*2)+1/(2*3)+1/*(5*6)+1/(6*7)+1/(7*8)+1/(8*9)
=(1-1/2)+(1/2-1/3)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1-1/2+1/2-1/3+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1-1/3++1/5-1/9
=(135-45+27-15)/135
=102/135