The infinite spell of 2016

Algebra Level 3

Let \(\displaystyle p(m) = \displaystyle \sum_{k=0}^\infty \dfrac1{m^k} \) and let \( \displaystyle x = \prod_{r=2}^{2016} p(r) \). Find \( \dfrac{x!}{2014!} \cdot \dfrac1{2015} \).

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