The complex series is $$\sum_{k=1}^{\infty} (i^k-\frac{1}{k^2})$$ I know the answer is that the series diverges.
Is this because $$\lim_{k\to\infty} (i^k-\frac{1}{k^2})$$ Does not exist since $i^k$ repeats itself infinitely? So it diverges by the kth term test for divergence?