Why do I love 2015 so much 1

Algebra Level 4

S=∑a=12015(∑b=12015(−1)a−12b)∑c=120151c \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 4030S4030S upto three correct places of decimals.

Inspiration.

This problem is a part of this set.
Akshat Sharda by Akshat Sharda
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