Let $(U_n)_{n \geqslant 1}$ be a sequence of mutually independent random variables following a Bernoulli distribution with parameter $1/2$. We set $Y_n = \sum_{k=1}^{n} \frac{U_k}{2^k}$, $F_n(x) = \mathbb{P}(Y_n \leqslant x)$ and $G_n(x) = \mathbb{P}(Y_n < x)$.
Using the monotonicity established in Q24, deduce the pointwise convergence of the sequences of functions $(F_n)_{n \geqslant 1}$ and $(G_n)_{n \geqslant 1}$.