(1)

\begin{align*} \left(2n\right)!! & =\prod_{k=1}^{n}2k\\ & =2^{n}\prod_{k=1}^{n}k\\ & =2^{n}n! \end{align*}

(2)

\begin{align*} \left(2n+1\right)!! & =\prod_{k=1}^{n}\left(2k+1\right)\\ & =2^{n}\prod_{k=1}^{n}\left(k+\frac{1}{2}\right)\\ & =2^{n}\prod_{k=1}^{n}\frac{\left(k+\frac{1}{2}\right)!}{\left(k-\frac{1}{2}\right)!}\\ & =2^{n}\frac{\left(n+\frac{1}{2}\right)!}{\left(\frac{1}{2}\right)!}\\ & =2^{n+1}\frac{\left(n+\frac{1}{2}\right)!}{\Gamma\left(\frac{1}{2}\right)} \end{align*}