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Power Serieseasy
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Using the binomial series (1+u)r=1+ru+r(r−1)2!u2+r(r−1)(r−2)3!u3+⋯(1+u)^r = 1 + ru + \frac{r(r-1)}{2!}u^2 + \frac{r(r-1)(r-2)}{3!}u^3 + \cdots(1+u)r=1+ru+2!r(r−1)​u2+3!r(r−1)(r−2)​u3+⋯, what are the first three terms of the Maclaurin series for 1+x\sqrt{1+x}1+x​?