Answer
$a_{1}=1$, $a_{2}=\displaystyle \frac{1}{2}$, $a_{3}=\displaystyle \frac{2}{3}$, $a_{4}=\displaystyle \frac{3}{5}$, $a_{5}=\displaystyle \frac{5}{8}$
Work Step by Step
$a_{1}=1$,
$.\displaystyle \qquad a_{n}=\frac{1}{1+a_{n-1}}$
$a_{2}=\displaystyle \frac{1}{1+1}=\frac{1}{2}$
$a_{3}=\displaystyle \frac{1}{1+\frac{1}{2}}=\frac{1}{\frac{2+1}{2}}=\frac{2}{3}$
$a_{4}=\displaystyle \frac{1}{1+\frac{2}{3}}=\frac{1}{\frac{3+2}{3}}=\frac{3}{5}$
$a_{5}=\displaystyle \frac{1}{1+\frac{3}{5}}=\frac{1}{\frac{5+3}{5}}=\frac{5}{8}$