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|+|1/5-1/4|+···+|1/10-1/9|
=1-1/2+1/2-1/3+1/3-1/4+…………1/9-1/10
=1+(1/2-1/2)+(1/3-1/3)+…………+（1/9-1/9）-1/10
=1-1/10
=9/10

|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+···+|1/10-1/9|
=1-1/2+1/2-1/3........+1/9-1/10=1-1/10=9/10

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