1/2+...................+71/72
=(1-1/2)+......................+(1-1/72)
=1+1+.....+1-1/2-...................-1/72
=8-(1/2+...................+1/72)
=8-(2-1/1*2+3-2/2*3+.............+9-8/8*9)
=8-(1-1/2+1/2-1/3+1/3-..............+1/8-1/9)
=8-(1-1/9)
=8-8/9
=64/9