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Here's a sneaky one: what happens if you take the derivative of \(\frac{1}{1-x}\text{?}\) We get \(\frac{1}{(1-x)^2}\text{.}\) On the other hand, if we differentiate term by term in the power series, we get \((1 + x + x^2 + x^3 + \cdots)' = 1 + 2x + 3x^2 + 4x^3 + \cdots\) which is the generating series for \(1, 2, 3, 4, \ldots\text{.}\) This says