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+1/2×1/3+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

(1/2018-1)(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

|1/2-1/3|+|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

原式=(1+1/2)(1-1/2)(1+1/3)(1-1/3)........(1+1/2015)(1-1/2015)(1+1/2016)(1-1/2016) =(3/2)(1/2)(4/3)(2/3)........(2016/2015)(2014/2015)(2017/2016)(2015/2016) =(1/2)*(2017/2016) =2017/4032

|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+3+5=3×3=9=(1+5)/2的平方.所以1++47+1++47=24²×2=1152。

1/2+1/2*3+1/3*4+...+1/2016*2017 =1/2+(1/2-1/3)+(1/3-1/4)+...(1/2016-1/2017) =1/2+1/2-1/3+1/3-1/4+...1/2016-1/2017 =1/2+1/2-1/2017 =2016/2017

原式=1/3+1/(2×4)+1/(3×5)+1/(4×6)+.....+1/(2017×2019) =1/3+1/2(1/2-1/4)+1/2(1/3-1/5)+1/2(1/4-1/6)+....+1/2(1/2017-1/2019) =1/3+1/4-1/8+1/6-1/10+1/8-1/12+....+1/4034-1/4038 =1/3+1/4+1/6+(1/8+1/10+....+1/4034)-(1/...

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