[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Using the Binomial Theorem, show that

[[math]] {1\over{\sqrt {1 - 4x}}} = \sum_{m = 0}^\infty {2m \choose m} x^m\ . [[/math]]

What is the interval of convergence of this power series?