Answer
$\frac{1}{2},\frac{1}{6},\frac{1}{24},\frac{1}{120},\frac{1}{720}$
Work Step by Step
To find the first five terms of the sequence $a_n = \frac{1}{(n+1)!}$, we must plug in $n=1, n=2, n=3, n=4,$ and $n=5.$
$a_1 = \frac{1}{(1+1)!}=\frac{1}{2!}=\frac{1}{2}$
$a_2 =\frac{1}{(2+1)!}=\frac{1}{3!}=\frac{1}{6}$
$a_3 =\frac{1}{(3+1)!}=\frac{1}{4!}=\frac{1}{24}$
$a_4 = \frac{1}{(4+1)!}=\frac{1}{5!}=\frac{1}{120}$
$a_5 = \frac{1}{(5+1)!}=\frac{1}{6!}=\frac{1}{720}$
Hence we see that the first five terms are $\frac{1}{2},\frac{1}{6},\frac{1}{24},\frac{1}{120},\frac{1}{720}$
