Answer
Absolutely converges
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{(k+1)!}{(2k-1)!} \times \dfrac{(2(k+1)-1)!!}{(k+1)!}\\=\lim\limits_{k \to \infty} \dfrac{k+1}{(2k+1)(2k)} \\=0 \lt 1$
So, we can conclude that the given series absolutely converges by the ratio test.
