(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)
=(14/28-10/30)+(7/28-6/30)+(4/28-3/30)+(2/28-2/30)+(1/28-1/30)
=(14+7+4+2+1)/28-(10+6+3+2+1)/30
=1-22/30
=4/15