计算|1/2-1+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+···+|1/10-1/9|.用递等式进行计算

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计算|1/2-1+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+···+|1/10-1/9|.用递等式进行计算计算|1/2-1+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|

计算|1/2-1+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+···+|1/10-1/9|.用递等式进行计算
计算|1/2-1+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+···+|1/10-1/9|.
用递等式进行计算

计算|1/2-1+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+···+|1/10-1/9|.用递等式进行计算
|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)+.+(1/8-1/9)+(1/9-1/10)
=1-1/2+1/2-1/3+.+1/8-1/9+1/9-1/10
=1-1/10
=9/10