it turns out that if I take some number, call it x, and that number is between 0 and 1, then
\(1 + x + x^2 + x^3 + \dots = \dfrac{1}{1-x}\)
if as in this case x=1/2 we have
\(1 + \dfrac 1 2 + \dfrac 1 4 + \dfrac 1 8 + \dots = \dfrac{1}{1-\dfrac 1 2}= 2\)
and subtracting 1 from both sides
\(\dfrac 1 2 + \dfrac 1 4 + \dfrac 1 8 + \dots = 1\)
Now you know some math I bet your friends don't!
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