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I am trying to determine the convergence/divergence of

Ʃ_{n=1}^{∞}i^{n}/n.

I have tried all the tests I could think of (Comparison, Ratio, Root, n^{th}term) and cannot determine it's convergence.

If there was a formula, for say, the Mth partial sum S_{M}then, if the limit as M → ∞ of S_{M}is L, we have convergence to L but I can't seem to arrange for the thing to add up the first M terms.

Clearly, I think something can be done with the fact that i^{n}= {i, -1, -i, 1} repeatably with periodicity 4. I'm not sure how this can exactly be of help though!

Any help appreciated, thanks.

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# Tricky Complex Series

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