Real numbers/Convergent sequence/Average sequence/Exercise

Let ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ be a convergent real sequence with limit ${}x$. Show that the sequence defined by

${}y_{n}:={\frac {x_{0}+x_{1}+\cdots +x_{n}}{n+1}}\,$

also converges to ${}x$.

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