Power Series

[Draq]

I was told to find the radius of convergence and interval of convergence of the series.
So far i have applied the Ratio Test for this series and have gotten stuck on the process.

This is what i have done so far

I cant figure out what to do with the limit portion, or how to deal with that fraction.
I would appreciate any help on what to do from here and would like to know if what I have done is correct so far.
If there is different approaches I could have taken towards this series please let me know. (such as other tests instead of ratio).

 

[Romsek]

divide top and bottom by \(\displaystyle n^3\)

it should then be clear what pieces go to zero and what the ultimate ratio on the left is.

That will leave you with some factor times |x-4| which you then use to establish the interval of convergence.

 

[Steven G]

Hmm, I would divide top and bottom by n^4. That will leave you with some factor times |x-4| which you then use to establish the interval of convergence.