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Real numbers/Bounded sequence/Zero sequence/Product/Fact/Proof/Exercise
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Real numbers
Let
(
x
n
)
n
∈
N
{\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} }}
be a null sequence and let
(
y
n
)
n
∈
N
{\displaystyle {}{\left(y_{n}\right)}_{n\in \mathbb {N} }}
be a bounded real sequence. Show that also the product sequence
(
x
n
y
n
)
n
∈
N
{\displaystyle {}(x_{n}y_{n})_{n\in \mathbb {N} }}
is a null sequence.
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