D= $\frac{3}{1×3}$ + $\frac{3}{3×5}$ + $\frac{3}{5×7}$ + ...+ $\frac{3}{2017×2019}$
= 3× { $\frac{1}{3}$ + $\frac{1}{3×5}$ + $\frac{1}{5×7}$ + ...+ $\frac{1}{2017×2019}$}
⇒ 2×D= 3×2×{ $\frac{1}{3}$ + $\frac{1}{3×5}$ + $\frac{1}{5×7}$ + ...+ $\frac{1}{2017×2019}$}
2×D= 3× { $\frac{2}{3}$ + $\frac{2}{3×5}$ + $\frac{2}{5×7}$ + ...+ $\frac{2}{2017×2019}$}
2×D= 3×{ 1- $\frac{1}{3}$ + $\frac{1}{3}$- $\frac{1}{5}$ +....+ $\frac{1}{2017}$ - $\frac{1}{2019}$ }
2×D= 3× { 1- $\frac{1}{2019}$ }
2×D= 3 × $\frac{2018}{2019}$
2×D= $\frac{2018}{673}$
⇒ D= $\frac{2018}{673}$ × $\frac{1}{2}$
= $\frac{1009}{673}$
