Question

Find the first four terms of the sequence whose nth term is $\frac{n^2}{n+1}$.

Answer 1

Given that: $T_n=\frac{n^2}{n+1}$
Then $T_1=\frac{1^2}{1+1}=\frac{1}{2},T_2=\frac{2^2}{2+1}=\frac{4}{3},T_3=\frac{3^2}{3+1}=\frac{9}{4},T_4=\frac{4^2}{4+1}=\frac{16}{5}$
$\therefore$ The first four terms of the sequence are $\frac{1}{2},\frac{4}{3},\frac{9}{4},\frac{16}{5}$.