Answer
{$2,~\frac{2}{3},~\frac{2}{5},~\frac{2}{7},~\frac{2}{9}$}
Work Step by Step
$a_{1}=2,~a_{n+1}=\frac{a_{n}}{1+a_{n}}$
$n=1$:
$a_{2}=\frac{a_{1}}{1+a_{1}}=\frac{2}{1+2}=\frac{2}{3}$
$n=2$:
$a_{3}=\frac{a_{2}}{1+a_{2}}=\frac{\frac{2}{3}}{1+\frac{2}{3}}=\frac{\frac{2}{3}}{\frac{5}{3}}=\frac{2}{5}$
$n=3$:
$a_{4}=\frac{a_{3}}{1+a_{3}}=\frac{\frac{2}{5}}{1+\frac{2}{5}}=\frac{\frac{2}{5}}{\frac{7}{5}}=\frac{2}{7}$
$n=4$:
$a_{5}=\frac{a_{4}}{1+a_{4}}=\frac{\frac{2}{7}}{1+\frac{2}{7}}=\frac{\frac{2}{7}}{\frac{9}{7}}=\frac{2}{9}$
