Question: 2016 Fall Final - 8

Author: Michiel Smid

Consider the following recursive function:

f(0) = $1$,
f(n) = $\frac{5}{n} \cdot f(n - 1)\; \ \text{for all}$ $\mathrm{integers}\ n \geq 1$.

Which of the following is true for all $n \geq 0$?

(a)

$f(n) = \frac{5}{n!}$

(b)

$f(n) = \frac{5^{n}}{n!}$

(c)

$f(n) = \frac{5^{n}}{(n+1)!}$

(d)

$f(n) = \frac{5^{n+1}}{n!}$