# Going Beyond

Calculus Level pending

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 $$i = \sqrt{-1}$$.

×