1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
=2(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=2(1/2-1/3+1/3-1/4+1/4-1/5+.+1/9-1/10)
=2x(1/2-1/10)
=4/5