What's your favorite proof accessible to a general audience? What math statement with proof do you  find most beautiful and   elegant, where such is  accessible to a general audience, meaning you could state, prove, and explain it to a general audience in roughly $5 \pm\epsilon$  minutes. 
Let's define 'general audience' as approximately  an average adult with education and experience comparable to someone holding a bachelor's degree in any non science major (e.g. history) from an average  North American university.

The harmonic series diverges because otherwise there exists a finite number 
\begin{align*}
S
&= 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\dotsb \\
&= \left(1+\frac{1}{2}\right)+\left(\frac{1}{3}+\frac{1}{4}\right)+\left(\frac{1}{5}+\frac{1}{6}\right)+\dotsb \\
&> \left(\frac{1}{2}+\frac{1}{2}\right)+\left(\frac{1}{4}+\frac{1}{4}\right)+\left(\frac{1}{6}+\frac{1}{6}\right)+\dotsb \\
&= 1+\frac{1}{2}+\frac{1}{3}+\dotsb \\
&= S
\end{align*}
