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\lhead{\bf Advanced Calculus (MAA 4211)}
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\rhead{Due Wednesday 10/19}
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\Problem By carefully negating the definition of convergence, state what it means for the sequence $(a_n)$ from the metric space $(X,d)$ to diverge. Your statement should begin ``The sequence $(a_n)$ from $(X,d)$ diverges if and only if for every $L\in X$...''.

\Problem Suppose $(a_n)$ is a sequence from $(\mathbb{R},d_1)$. Show that if $(a_n)$ converges to $L$ then its sequence of \emph{Cesaro means} $(s_n)$ defined by
\[
	s_n=\frac{1}{n+1}\sum_{i=0}^n a_i
\]
also converges to $L$. Also give an example of a divergent sequence $(a_n)$ whose Cesaro means converge.

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