# Summing Up The Nearest!

Calculus Level 5

$\large \displaystyle \sum_{n=1}^{\infty} \frac{1}{\lfloor \sqrt[4]{n} \;\rceil ^7}$

The above sum can be expressed as $$\frac{a}{b}\pi^{\alpha} + \frac{c}{d}\pi^{\beta}$$, where $$a,b,c,d,\alpha ,$$ and $$\beta$$ are positive integers, with $$a$$ and $$b$$ being co-prime, $$c$$ and $$d$$ are co-prime.

Find $$a+b+c+d+\alpha +\beta$$.

Details and Assumptions:

$$\bullet \lfloor x \rceil$$ denotes the nearest integer to $$x$$ .

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