Answer
Divergent
Work Step by Step
Let us consider that $\lim\limits_{k \to \infty}a_k=\lim\limits_{k \to \infty} \dfrac{(-1)^n}{0.9^n})\\=\lim\limits_{k \to \infty}(- \dfrac{1}{0.9})^n\\=\lim\limits_{k \to \infty} (\dfrac{-10}{9})^n$
This shows a divergent geometric sequence.
