# Somersaults are more fun than this sum assault

Calculus Level 2

$\sum_{n=0}^{\infty} \frac{1}{(4n)!}$

The above sum can be expressed in the form

$\frac{1}{n} \left( \sum_{k=1}^{mn} e^{i^{k}} \right)$

where $$i$$ is the imaginary unit and $$n$$ is some positive multiple of 4.

Find $$m$$.

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