Convergence of a power series

Determine the values of $x$ for which the following series is convergent or divergent: $1+\frac{1}{2}\cdot \frac{x^2}{4}+\frac{1\cdot 3}{2\cdot 4}\cdot \frac{x^4}{8}+\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\cdot \frac{x^6}{12}+\dots$

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.b, No. 1