[tex] e^{i\pi}=-1 [/tex](adsbygoogle = window.adsbygoogle || []).push({});

I was wondering how on earth this was possible. I know that:

[tex]

e^z = 1 + z + \frac{z^2}{2!} + \frac{z^3}{3!}+...+\frac{z^n}{n!}

[/tex]

So

[tex]

e^{i\pi}=1+i\pi+\frac{-\pi^2}{2!}+\frac{-\pi^3i}{3!}+\frac{\pi^4}{4!}...

[/tex]

I was wondering if there is any way to solve this other than punching out actual numbers and seeing about where they converge to?

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# Solve this other than punching out actual numbers

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