Interval of Convergence for Infinite Series with Ratio Test

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Homework Statement

Find the Interval of Convergence for the given series. Check the endpoint behavior carefully sigma[n=0,inf] (n (x-2)^n)/( (n+1)4^n )

Homework Equations

The Attempt at a Solution

I was following along with the answer key and they used the ratio test...
The only problem is that
[x/4 - 1/2] lim n->inf (n+1)^2 / ((n^2 + 2n) ) = x/4 - 1/2
because the lim n->inf (n+1)^2 / ((n^2 + 2n) )
I thought the ratio test was inconclusive if when you took the limit you got 1?
The answer key than proceeded to solve for x assuming
x/4 - 1/2 < 1
can this be done even though the limit equals one?

 

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My bad... I get it now sorry guys...