S = $\frac{3}{1.3}$ + $\frac{3}{3.5}$ + ... + $\frac{3}{2013.2015}$
= 3($\frac{1}{1.3}$ + $\frac{1}{3.5}$ +... + $\frac{1}{2013.2015}$)
= $\frac{3}{2}$ ($\frac{2}{1.3}$ + $\frac{2}{3.5}$ + ... + $\frac{2}{2013.2015}$)
= $\frac{3}{2}$ ( 1 - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{5}$ + ... + $\frac{1}{2013}$ - $\frac{1}{2015}$)
= $\frac{3}{2}$ (1 - $\frac{1}{2015}$)
= $\frac{3}{2}$ . $\frac{2014}{2015}$
= $\frac{3021}{2015}$