Questions tagged [cesaro-summable]

For questions about Cesàro summation and Cesàro summable sequences.

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Cesáro summation, prove convergence [closed]

Prove that if $a_k≥0$ and $\Sigma \, a_k$ is $(C,1)-summable$ (Cesáro summable), then the series is convergent in the usual sense. (Assume the contrary – what does that entail for a positive series?) ...
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Summarise with Cesaro summation [closed]

Lets consider series $A = \sum_{n=0}^\infty(-1)^n$. $A = 1 - 1 + 1 - 1 \dots$ Lets consider k-th term of series A. Move it to $2^kth$ position. So, and repeat it for every term in series. Obviously, ...