Mistaken Identity

Calculus Level 3

\[ \large n = \left(\sum_{r=0}^\infty \dfrac1{r!} \right)^{8i \sum_{k=1}^\infty \frac{ (-1)^{k+1}}{2k-1}} \]

Evaluate \(n\) to 3 significant figures.

\[\] Notation: \(i=\sqrt{-1}\) is the imaginary unit.

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