https://www.quora.com/Mathematics-What-is-the-most-beautiful-theorem-proof-and-why

I am sure that there are some out there that would say that this does not constitute a proof, but I have always found this to be a beautiful *justification* for the following identity.

∑n=1∞12n=1∑n=1∞12n=1

Proof:

I always show this to my students at the beginning of sequences and series.