Calculus 8th Edition

Radius of convergence is $\sqrt R$
Let $x^{2}=y$., then $\sum_{n=1}^{\infty}c_{n}x^{2n}=\sum_{n=1}^{\infty}c_{n}y^{n}$ So it is convergent for $-R\lt y\lt R$ , therefore, for $x$ it is convergent of $-\sqrt R\lt x\lt \sqrt R$ Hence, Radius of convergence is $\sqrt R$