Let $\displaystyle \Sigma_{k=0} ^\infty a_k x^k$ and $\displaystyle \Sigma _{k=0} ^\infty b_k x^k$ be real power series which converge for $\displaystyle |x|<1$. If $\displaystyle \Sigma_{k=0} ^\infty a_k x^k$= $\displaystyle \Sigma _{k=0} ^\infty b_k x^k$ for $\displaystyle x=1/2,1/3,1/4,...$, then prove that $\displaystyle a_k=b_k$ for all $\displaystyle k$