Radicals are getting crazy in 2016

Algebra Level 4

If n=120161nn+1+(n+1)n=a1a,\large \displaystyle \sum_{n=1}^{2016} \dfrac{1}{n\sqrt{n+1}+(n+1)\sqrt{n}} = \dfrac{\sqrt{{a}}-1}{\sqrt{{a}}}, find aa.


Inspiration.

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