- #1
ehrenfest
- 2,020
- 1
Homework Statement
Investigate the behavior (convergence or divergence) of [itex]\sum_n 1/(1+z^n)[/itex] where z is complex.
Homework Equations
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?