#### Answer

$a_1=\frac{1}{2}$
$a_2=\frac{4}{3}$
$a_3=\frac{9}{4}$
$a_4=\frac{16}{5}$
$a_{10}=\frac{100}{11}$

#### Work Step by Step

We are given:
$a_{n}= \frac{n^{2}}{n+1}$
We evaluate:
$a_1= \frac{1^{2}}{1+1}=\frac{1}{2}$
$a_2=\frac{2^{2}}{2+1}=\frac{4}{3}$
$a_3=\frac{3^{2}}{3+1}=\frac{9}{4}$
$a_4= \frac{4^{2}}{4+1}=\frac{16}{5}$
$a_{10}= \frac{10^{2}}{10+1}=\frac{100}{11}$