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**1. Homework Statement**

Investigate the behavior (convergence or divergence) of [itex]\sum_n 1/(1+z^n)[/itex] where z is complex.

**2. Homework Equations**

**3. The Attempt at a Solution**

If the modulus of z is less than 1, it is not hard to show that the limit of the sequence is not 0 (it is actually not finite) and thus the series cannot converge. But if the modulus of z is greater than or equal to 1, I don't what to apply. The root test? The ratio test? The comparison test?