With the notation and setup of the previous questions (mutually independent Rademacher variables, $S_N = \sum_{n=0}^N X_n a_n$), conclude that the event $$\left\{\text{the series } \sum X_n a_n \text{ is convergent}\right\}$$ has probability 1.
With the notation and setup of the previous questions (mutually independent Rademacher variables, $S_N = \sum_{n=0}^N X_n a_n$), conclude that the event
$$\left\{\text{the series } \sum X_n a_n \text{ is convergent}\right\}$$
has probability 1.