I love being inspired! (Part-2)

Algebra Level 5

\[\Large{ S = \displaystyle \sum_{n=1}^{2015} \dfrac{n^{ \left(\log_{\frac{n+1}{n}} (n) \right)}}{(n+1)^{ \left( \log_{\frac{n+1}{n}} (n+1) \right)}} }\]

If \(S\) can be expressed as \(\dfrac{A}{B}\), where \(A,B\) are positive co-prime integers, find \(A+B\).

This problem is made by me and my friend Akshat Sharda.
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