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, there are positions in new series which are empty. Denote their by zero.

So, what is the sum of new series if we summarise with Cesaro summation?


closed as off-topic by Batominovski, TheGeekGreek, Lord Shark the Unknown, Claude Leibovici, Parcly Taxel May 10 '17 at 7:30

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    $\begingroup$ Utterly unintelligible. Rewrite more clearly. $\endgroup$ – Martín-Blas Pérez Pinilla Apr 26 '17 at 6:48
  • $\begingroup$ @Martín-BlasPérezPinilla, Is it more clearly? $\endgroup$ – marka_17 May 9 '17 at 17:06

Hint: the partial sums $S_n$ can be $1$ or $0$. What will be $S_n/n$?


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