(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)

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/24 02:51:46
(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)
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(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)+(1/4-1/5)+(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)+(1/4-1/5)+(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

（1/2-1/3)+(1/4-1/5)+(1/7-1/10)+(1/14-1/15)+(1/28-1/30)
=1/6+1/20+3/70+1/210+1/420
=13/60+1/21+1/420
=112/420
=28/105