Answer
Converges absolutely
Work Step by Step
Apply the ratio test.
Therefore, $ L=\lim\limits_{k \to \infty} |\dfrac{a_{k+1}}{a_k}|=\lim\limits_{k \to \infty} \dfrac{1}{(k+1)!} \times \dfrac{k!}{1}\\=\lim\limits_{k \to \infty} \dfrac{k !}{(k+1)!} \\=\lim\limits_{k \to \infty} \dfrac{1}{k+1} \\=0 \lt 1$
So, we can conclude that the given series converges absolutely by the ratio test.
