Chapter 11.3, Problem 51E

Working with binomial series Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Maclaurin series for the following functions. Give the interval of convergence for the new series (Theorem 11.4 is useful). Use the Maclaurin series

$\sqrt{1+x}=1+\frac{x}{2}-\frac{x^2}{8}+\frac{x^3}{16}-\mathrm{...},\text{ for -1 }\le x\le \text{ 1}$

51. $\sqrt{1+x^2}$