Let $f$ be analytic on ball $B_R \left( 0 ight)$ and $f \left( z ight) = \sum_{n=0}^\infty a_n z^n$ for $\abs{z} < R$. We wish to show that if $f_n \left( z ight) = \sum_{k=0}^n a_k z^k$, then $f_n \to f$ in $C \left( G, \mathbb{R} ight)$