Question: 2016 Fall Midterm - 10
The function $f : \mathbb{N} \rightarrow \mathbb{R}$ is defined by
$$
\begin{align}
f(0) &= 7, \\
f(n) &= \frac{n}{3} \cdot f(n - 1)\; \ \mathrm{for}\ n \geq 1.
\end{align}
$$
What is $f(n)$?
(a)
$f(n) = 7^n \cdot \frac{(n + 1)!}{3^n}$
(b)
$f(n) = 7^n \cdot \frac{n!}{3^n}$
(c)
$f(n) = 7 \cdot \frac{n!}{3^n}$
(d)
$f(n) = 7 \cdot \frac{(n + 1)!}{3^n}$