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.

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