Let $a > 0$, $I = [-a, a]$, and $f(x) = \dfrac{1}{1+x^2}$ for $x \in \mathbb{R}$. For all $n \in \mathbb { N } ^ { * }$, let $P _ { n } = \Pi _ { n } ( f )$ be the Lagrange interpolation polynomial of $f$ on $I$. Show that, if $a < \frac { 1 } { 2 }$, the sequence of polynomials $\left( P _ { n } \right) _ { n \in \mathbb { N } ^ { * } }$ converges uniformly towards $f$ on $[ - a , a ]$.