\text { Prove that if the nonnegative series } \sum_{n \in \mathbb{N}} a_{n} \text { and } \sum_{n \in \mathbb{N}} b_{n} \text { converge, then so } \text{ does the series }\sum_{n\in\mathbb{N}}a_nb_n\text{. } \text { Deduce that if the nonnegative series } \sum_{n \in \mathbb{N}} a_{n} \text { converges, then so does the } \text { series } \sum_{n \in \mathbb{N}} a_{n}{ }^{2} \text {. }

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