Answer
$a_1=1$
$\displaystyle a_2=\frac{1}{2}$
$\displaystyle a_3=\frac{1}{6}$
$\displaystyle a_4=\frac{1}{24}$
$\displaystyle a_5=\frac{1}{120}$
$\displaystyle a_6=\frac{1}{720}$
$\displaystyle a_7=\frac{1}{5040}$
Work Step by Step
We are given:
$\displaystyle a_{n}= \frac{a_{n-1}}{n}$ and $a_1=1$
We evaluate:
$a_1=1$
$\displaystyle a_2=\frac{a_{1}}{2}=\frac{1}{2}$
$\displaystyle a_3=\frac{a_{2}}{3}=\frac{1}{2*3}=\frac{1}{6}$
$\displaystyle a_4=\frac{a_{3}}{4}=\frac{1}{6*4}=\frac{1}{24}$
$\displaystyle a_5=\frac{a_{4}}{5}=\frac{1}{24*5}=\frac{1}{120}$
$\displaystyle a_6=\frac{a_{5}}{6}=\frac{1}{120*6}=\frac{1}{720}$
$\displaystyle a_7=\frac{a_{6}}{7}=\frac{1}{720*7}=\frac{1}{5040}$
