# Interesting problem

Algebra Level 4

$\sqrt{1+\frac 1{1^2} + \frac 1{2^2}} + \sqrt{1+\frac 1{2^2} + \frac 1{3^2}} + \sqrt{1+\frac 1{3^2} + \frac 1{4^2}} + \cdots + \sqrt{1+\frac 1{2014^2} + \frac 1{2015^2}}$

If the sum above can be expressed as $$\dfrac {ab}c$$, where $$a$$, $$b$$ and $$c$$ are positive integers with $$ab$$ and $$c$$ being coprime integers and $$a = b+2$$. Find $$a+b+c$$.

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