Chapter 9.3, Problem 50E

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 9.4 is useful). Use the Maclaurin series

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

50. $\sqrt{4-16x^2}$