求|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/10-1/9|的值

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求|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/10-1/9|的值
求|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/10-1/9|的值

求|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/10-1/9|的值
|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/10-1/9|
=1-1/2+1/2-1/3+1/3-1/4+·····+1/9-1/10
=1-1/10
=9/10
就是裂项求和...