Limited edition

Calculus Level 4

limα0ecos(αn)eαm=e2\large \lim_{\alpha\rightarrow 0}\frac{e^{\cos(\alpha^{n})}-e}{\alpha^{m}} = -\frac{e}{2}

Let mm and nn be two constant positive integers greater than 1 such that the equation above holds true.

Find the ratio mn \frac{m}{n} .

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