To find the sum of \(1-1+1-1+...\) we take the artithmetic mean of the cycling results, by which we obtain \(1/2\). Using this logic, what is the value we obtain when evaluating \(i\) taken to successive powers of integers towards infinity?

Moderator's edit: I think he/she wants to calculate the Cesaro sum of \(\displaystyle \lim_{n\to\infty} \dfrac1n\sum_{k=1}^n i^k\) where \(i = \sqrt{-1} \).

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