A power series is an infinite sum of the type $\sum_{n=0}^{\infty} a_n t^n$ for some (real? complex? depending on the context) $a_n$.
In the case where $a_n=0$ for all $n\
ot=2$ and $a_2=1$ you would get that $\sum_{n=0}^{\infty} a_n t^n=t^2$, and so it is a power series. Do note that this specific power series absolutely converges for all $t$.