# Convergence of Ceasaro Mean Implies convergence of the original sequence

I have seen in a paper to use the fact that convergence in Ceasaro Mean [Ceasaro Mean] (http://en.wikipedia.org/wiki/Ces%C3%A0ro_mean) implies convergence of the original sequence. This is not true in general. So, what additional condition we need to use to make this happen. Then I can check whether that condition is satisfied in the context ?