Let $\sum _ { k \geqslant 0 } c _ { k } x ^ { k }$ be a power series with radius of convergence $R > 0$, $f(x) = \sum_{k=0}^{+\infty} c_k x^k$ for $x \in ]-R, R[$, and $a > 0$. Assume that $a < R / 3$. Show that the sequence of polynomials $\left( P _ { n } \right) _ { n \in \mathbb { N } ^ { * } } = \left( \Pi _ { n } ( f ) \right) _ { n \in \mathbb { N } ^ { * } }$ converges uniformly towards $f$ on $[ - a , a ]$.