Interesting problem

Algebra Level 4

1+112+122+1+122+132+1+132+142++1+120142+120152\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 abc\dfrac {ab}c, where aa, bb and cc are positive integers with abab and cc being coprime integers and a=b+2a = b+2. Find a+b+ca+b+c.

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