# What is the radius of convergence of sum_1^oo (x^n ) / 6^n?

$6$
the series is $\frac{x}{6} + {\left(\frac{x}{6}\right)}^{2} + {\left(\frac{x}{6}\right)}^{3} + \ldots$, which is geometric.
geometric series converge if and only if $| r a t i o | < 1$.
the ratio is $\frac{x}{6}$.
the series will converge if and only if $| \frac{x}{6} | < 1 \rightarrow | x | < 6$
the radius of convergence is $6$