An algebra problem by Matías Bruna

Algebra Level pending

For each \( n \in \mathbb{N}\), are defined \( f(n) \) and \( g(n) \) as follows:

\( f(n)=2n+1 \) and \( g(n)=n^{2}+n \).

And let \( S=\dfrac{1}{\sqrt{f(1)+2\sqrt{g(1)}}} + \dfrac{1}{\sqrt{f(2)+2\sqrt{g(2)}}} + \cdots + \dfrac{1}{\sqrt{f(2015)+2\sqrt{g(2015)}}}\)

Compute \(\left \lfloor{10S}\right \rfloor \).

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