An Interesting Question I Posed to Myself About $\pi$ as an Average. https://ift.tt/eA8V8J

Prove or disprove:

There is a sequence $x$ with each $x_i\in\{1,2,3,4\}$ and $\pi$ can be written as the average $$\pi = \lim_{n\rightarrow\infty}\sum_{i=1}^{n}\frac{x_i}{n}$$

I am sure that this question would be trivial using advanced number theory concepts, but I would like a solution using just high-school olympiad level mathematics.

Thanks a lot. ☺

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