Convergence of a hypergeometric series

Determine the values of $x$ for which the following series is convergent or divergent: $1+\frac{3}{7}x+\frac{3\cdot 6}{7\cdot 10}{x}^2+\frac{3\cdot 6\cdot 9}{7\cdot 10\cdot 13}{x}^3+\frac{3\cdot 6\cdot 9\cdot 12}{7\cdot 10\cdot 13\cdot 16}{x}^4+\dots$

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.b, No. 2