www.ypnh.net > 1*1/2+1/2*1/3+1/3*1/4……+1/2017=

1*1/2+1/2*1/3+1/3*1/4……+1/2017=

1*1/2+1/2*1/3+1/3*1/4……+1/2017*1/2018 =1-1/2+1/2-1/3+1/3-1/4+……+1/2017-1/2018 =1-1/2018 =2017/2018

1*1/2+1/2*1/3+1/3*1/4……+1/2017*1/2018 =1-1/2+1/2-1/3+1/3-1/4+……+1/2017-1/2018 =1-1/2018 =2017/2018

=1-1/2+1/2-1/3+1/3-1/4+...+1/2016-1/2017 =1-1/2017 =2016/2017

(1/2018-1)(1/2017-1)...(1/3-1)(1/2-1) =-(1- 1/2018)(1- 1/2017)...(1- 1/3)(1- 1/2) =-(2017/2018)(2016/2017)...(2/3)(1/2) =-(2017×2016×...×2×1)/(2018×2017×...×3×2) =-1/2018

=1-1/2+1/2-1/3+1/3-1/4+…+1/2016-1/2017 =1-1/2017 =2016/2017 (2017分之2016) 你好,本题已解答,如果满意 请点右下角“采纳答案”。

约等于: 8.186830075

1+1/2×1/3+1/3×1/4+…+1/2016*1/2017 =1+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2016-1/2017 =1+1/2-1/2017 =4034/4034+2017/4034-2/4034 =6049/4034

|1-1/2|+|1/2-1/3|+|1/3-1/4|+……+|1/2017-1/2018| =(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2017-1/2018) =1-1/2018 =2017/2018

|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+...+|1/2016-1/2017| =1/2-1/3+1/3-1/4+1/4-1/5+……+1/2016-1/2017 =1/2-1/2017 =2015/4034

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