# 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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