Why do I love 2015 so much 1

Algebra Level 4

$\large{S = \dfrac{\displaystyle \sum^{2015}_{a=1} \left(\sum^{2015}_{b=1} \frac{(-1)^{a-1}}{2b} \right)}{\displaystyle \sum^{2015}_{c=1}\frac{1}{c}}}$

Evaluate the value of $4030S$ upto three correct places of decimals.

Inspiration.

Why do I love 2015 so much 1

This problem is a part of this set.