Real numbers/Bounded sequence/Zero sequence/Product/Fact/Proof/Exercise

Let ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ be a null sequence and let ${}{\left(y_{n}\right)}_{n\in \mathbb {N} }$ be a bounded real sequence. Show that also the product sequence ${}(x_{n}y_{n})_{n\in \mathbb {N} }$ is a null sequence.

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