I have redone this problem many times, and can't seem to figure it out!

The problem is to use the ratio test to find the limit and convergence of this series:

Now, using the ratio test, I come up with this:

How do I expand this to cancel the series out? This is what I tried:

However, when I cancel everything out, I get which results in the limit being 0.

But 0 is not the correct limit.

Any help would be very appreciated!