Alright I think I got it this time:
by Cesaro's mean (your sequence is ), so
Hey, thanks for the answer, there is still something unclear to me,
in order to use cesaro's mean, you assume that
at least by Cauchy Criterion For Convergence (to my knowledge) i find that this sequence does not have a limit.
i'd appreciate further explanations (also if i got the Cauchy criterion wrong... )
Thanks and have a nice weekend