Question 979404
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sum_{k=1}^\infty\,a_k\ =\ \frac{a}{1\ -\ r}\ \forall\ r\ :\ |r|\ <\ 1]


Where *[tex \Large a] is the first term and *[tex \Large r] is the common ratio.


Just do the arithmetic.


If *[tex \Large |r|\ \geq\ 1] then the series diverges.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it