Verify that the converse of (Cesàro) is not always true by exhibiting a sequence $\left( u _ { n } \right) _ { n \in \mathbb { N } } \in \mathbb { R } ^ { \mathbb{N} }$ that does not converge and such that $\left( \sigma _ { n } \right) _ { n \in \mathbb { N } }$ converges in $\mathbb { R }$.