Answer
True
Work Step by Step
Given $\sum c_nx^n$ diverges when $x=6$
Using the Ratio Test,
$\lim |\frac{c_{n+1}6^{n+1}}{c_n6^n}|>1$
$\lim |\frac{6c_{n+1}}{c_n}|>1$
(Multiply by $10/6$)
$\lim |\frac{10c_{n+1}}{c_n}|>\frac{10}{6}$
It implies that
$\lim |\frac{c_{n+1}10^{n+1}}{c_n10^n}|=\lim |\frac{10c_{n+1}}{c_n}|>\frac{10}{6}>1$
So, the series $\sum c_nx^n$ diverges when $x=10$.
