# Past, present, and everything in between

Algebra Level 5

$\Large \prod_{i=1}^{2^{2015}} \left( \sqrt[2^i]{2015} + \sqrt[2^i]{1995} \right)$

Given that the reciprocal of the product above can be expressed as $$\large \dfrac 1d \left( a^{1/2^b} - c^{1/2^b} \right)$$ where $$a,b,c$$ and $$d$$ are positive integers. What is the value of $$\large \dfrac{c \log_2( b) + 5a}{\log_2 (b^d)}?$$

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