=1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72
=8-1/(1x2)-1/(2x3)-1/(3x4)-1/(4x5)-1/(5x6)-1/(6x7)-1/(7x8)-1/(8x9)
=8-[1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)]
=8-[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9]
=8-(1-1/9)
=8-8/9
=7+1/9