Uniformly convergence of infinite series

Question

I need to find in which interval this infinite series is uniformly convergent.

$\sum_{n=1}^{\infty}(\frac{x-2}{6})^n$

I can see that it converges when $-4 < x <8$ but I can't figure out when it is uniformly convergent.

Useful choices: $-3.8 < x < 7.8$ and $-4 < x < 0$.

Anyone has some ideas?

Answer 1

This is a power series centered at $2$

The radius of convergence is $6$

So it converges uniformly at every compact subset of $(-4,8)$

So the only choice of the six, is the interval $[-3,8,7,8]$