Chapter 1.14, Problem 3P

In Problem 3 to 7, assume that the Maclaurin series converges to the function.

If $0<x<\frac{1}{2}$, show [using theorem (14.3)] that $\sqrt{1+x}=1+\frac{1}{2}x$ with an error less than 0.032. Hint: Note that the series is alternating after the first term.