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

问题描述:

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

(1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)
= 1/2 - 1/3 + 1/4 + (1/7 + 1/14 + 1/28) - (1/5 + 1/10 + 1/15 + 1/30)
= 1/2 - 1/3 + 1/4 + 7/28 - 12/30
= 1/2 - 1/3 + 1/4 + 1/4 - 2/5
= 1 - 1/3 - 2/5
= 2/3 - 2/5
= 4/15