One more that I am hung up on...
$\displaystyle
\sum^{\infty}_{n=2} (-\frac{n}{8})^n$
you need abs values here, just like the ratio test
BUT inside the root. You don't want the root of a negative number.
Whenever the entire term is to the n$\displaystyle ^{th}$ power it's easy to use the root test.