$(c)$ Suppose that $f(x)={\displaystyle \underset{n=0}{\overset{}{}}}{a}_n{x}^n$ and $g(x)={\displaystyle \underset{n=0}{\overset{}{}}}{b}_n{x}^n$ converges for all $xin$ some

interval containing $0$ and that $f(t_m)=g(t_m)$ for some sequence $\{t_m\}$ converging $to$

$0.$ Show that $a_n=b_n$ for each $n.$

$(In$ particular can have only one representation $as$ a power series centered $at0.)$