One out of two plus one out of six plus one out of twelve plus one out of twenty plus one out of thirty

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