# Math Help - alternating series #3

1. ## alternating series #3

One more that I am hung up on...

$
\sum^{\infty}_{n=2} (-\frac{n}{8})^n$

2. The root test is best here

3. Originally Posted by matheagle
The root test is best here
So I would have

$- \sqrt[n]{(\frac{n}{8})^n}$

$= -\frac{n}{8} = - \infty$ ????

4. 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 $^{th}$ power it's easy to use the root test.

5. you place the abs values here....

Originally Posted by mollymcf2009
So I would have

$\biggl|\biggl({-n\over 8}\biggr)^n\biggr|^{1/n}=\frac{n}{8}\to\infty>1$
Basically it shows you, like in the ratio test, that the terms (in absolute value) are getting bigger.
Hence they cannot be approaching zero.