(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)=1/2-(1/3-1/3)-(1/4-1/4)-..........-(1/7-1/7)-1/8=1/2-0-0-..-0-1/8=1/2-1/8=3/8