determine the radius of convergence and the interval of convergence of the power series as n goes from 1 to infinity of

((1-x)^2n) / ((4^n) * n)

This was on a test and I missed it. Somehow I got negative infinity to infinity. I would like to see the proper steps. thanks in advance..

2. Originally Posted by calculushelptx
determine the radius of convergence and the interval of convergence of the power series as n goes from 1 to infinity of

((1-x)^2n) / ((4^n) * n)

This was on a test and I missed it. Somehow I got negative infinity to infinity. I would like to see the proper steps. thanks in advance..
apply the root test. can you continue?

3. I applied the ratio test and got 1/4 < 1 but cannot continue with root.

4. Originally Posted by calculushelptx
I applied the ratio test and got 1/4 < 1 but cannot continue with root.
whatever you are applying, it is not the ratio test. by the ratio test, we get $\displaystyle \bigg| \frac {(1 - x)^2}4\bigg|<1$

now find the range for x. and remember to check the endpoints when finished