One out of two plus one out of six plus one out of twelve plus one out of twenty plus one out of thirty
1/2+1/6+1/12+1/20+1/30
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)
=1/2-1/6
=2/6
=1/3
1/2+1/6+1/12+1/20+1/30
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)
=1/2-1/6
=2/6
=1/3