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## Homework Statement

Test to see if [tex]\sum_{n=1}^{\infty}{ i^n/n }[/tex] converges.

## Homework Equations

See above.

## The Attempt at a Solution

If I separate this series into real/imag. parts both series diverges by the integral test. However, according to Wolfram Alpha, the series converges to [tex]\sum_{n=1}^{\infty}{ i^n/n }= -log(1-i)[/tex]

What test would I use to show this converges, and how did I misuse the integral test?

Thanks,

Chris Maness