Answer
$a_{1}=\displaystyle \frac{1}{2}$,
$a_{2}=\displaystyle \frac{4}{3}$,
$a_{3}=\displaystyle \frac{9}{4}$,
$a_{4}=\displaystyle \frac{16}{5}$,
$a_{10}=\dfrac{100}{11}$.
Work Step by Step
$a_{1}=\displaystyle \frac{1^{2}}{1+1}=\frac{1}{2}$,
$a_{2}=\displaystyle \frac{2^{2}}{2+1}=\frac{4}{3}$,
$a_{3}=\displaystyle \frac{3^{2}}{3+1}=\frac{9}{4}$,
$a_{4}=\displaystyle \frac{4^{2}}{4+1}=\frac{16}{5}$,
$a_{10}=\displaystyle \frac{10^{2}}{10+1}=\frac{100}{11}$.
