Sometimes, a picture is worth a thousand words:
We could, of course, multiply both sides of this equation by 2. This would give us:
[math]\frac{2}{2^1}+\frac{2}{2^2}+\frac{2}{2^3}+\frac{2}{2^4}+\frac{2}{2^5}+\frac{2}{2^6}+\frac{2}{2^7}+\frac{2}{2^8}+\frac{2}{2^9}+…\,=\,2.0[/math]
Did you notice that every numerator on the...
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