$\dfrac{3}{1.3} + \dfrac{3}{3.5} + \dfrac{3}{5.7} + ...... + \dfrac{3}{2015.2017}$
$= 3.(\dfrac{1}{1.3} + \dfrac{1}{3.5} + \dfrac{1}{5.7} + ...... + \dfrac{1}{2015.2017})$
$= \dfrac{3}{2}.(\dfrac{2}{1.3} + \dfrac{2}{3.5} + \dfrac{2}{5.7} + ...... + \dfrac{2}{2015.2017})$
$= \dfrac{3}{2}.(1- \dfrac{1}{3} + \dfrac{1}{3}-\dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{7} + ...... + \dfrac{1}{2015} - \dfrac{1}{2017})$
$= \dfrac{3}{2} . (1 - \dfrac{1}{2017})$
$= \dfrac{3}{2} . (\dfrac{2016}{2017})$
$= \dfrac{3024}{2017}$
