<s>[INST] 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.
 [/INST] Here's a variation on $$\sum_{n=1}^{R} n =\frac{R(R+1)}{2}$$ I stumbled onto this a while back. 

shows 
$$1+2+3+4+5+6+7 = \frac{1}{2}\cdot b\cdot h + \frac{1}{2}\cdot b$$
$$1+2+3+4+5+6+7 = \frac{1}{2}\cdot 7\cdot 7 + \frac{1}{2}\cdot 7$$
then $$1+2+3+4+5+6+7 = \frac{1}{2}\left( 7\cdot 7 +  7\right)$$
thus $$1+2+3+4+5+6+7 = \frac{7(7+1)}{2}$$
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