1 .
The function $f : \mathbb{Z}_{\geq 0} \rightarrow \mathbb{R}$ is defined by
$$
f(n) = \begin{cases}
7 & \text{if}\ n = 0 \\
\frac{n}{3} \cdot f(n - 1) & \text{if}\ n \geq 1
\end{cases}
$$
What is $f(n)$?
(a)
$f(n) = 7^n \cdot \frac{(n + 1)!}{3^n}$
(b)
$f(n) = 7 \cdot \frac{n!}{3^n}$
(c)
$f(n) = 7 \cdot \frac{(n + 1)!}{3^n}$
(d)
$f(n) = 7^n \cdot \frac{n!}{3^n}$