1/1*3+1/3*5+1/5*7+...+1/2017*2019
急
因为：
1/[2n-1）（2n+1）]
=1/2× [1/(2n-1)-1/(2n+1)]
所以：
原式
=1/2×(1/1-1/3+1/3-1/5+1/5-1/7+……+1/2017-1/2019)
=1/2×(1-1/2019)
=1/2×2018/2019
=1009/2019
1/(1*3)+1/(3*5)+1/(5*7)+.......+1/(2017*2019)
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+……+1/2*(1/2017-1/2019）
=1/2*(1-1/3+1/3-1/5+1/5-1/7+……+1/2017-1/2019)
=1/2*(1-1/2019)
=1/2*2018/2019
=1009/2019
1/(1×3)+1/(3×5)+1/(5×7)+...+1/(2017×2019)
=1/2×[2/(1×3)+2/(3×5)+2/(5×7)+...+2/(2017×2019)]
=1/2×(1-1/3+1/3-1/5+1/5-1/7+…+1/2017-1/2019)
=1/2×(1-1/2019)
=1/2×2018/2019
=1009/2019
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