Convergence of a power series with even powers

Determine the values of $x$ for which the following series is convergent or divergent: $x^2+\frac{2^2}{3\cdot 4}{x}^4+\frac{2^2\cdot 4^2}{3\cdot 4\cdot 5\cdot 6}{x}^6+\frac{2^2\cdot 4^2\cdot 6^2}{3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8}{x}^8+\dots$

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.b, No. 3