# 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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