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Feb 28, 2013 at 18:46 vote accept FelipeG
Nov 12, 2012 at 20:05 comment added FelipeG Thanks, I was not looking for the case when the cesaro means do not converge. I wanted that as a part of the hypothesis. But I think your counter example works, if you take $x_{n}$=0 only sporadically, then you will have cesaro mean convergence but not convergence.
Nov 10, 2012 at 3:17 history answered Alexandre Eremenko CC BY-SA 3.0