I'm asked to specifically use the Ratio Test (formula below) to determine whether this series converges or diverges (if it converges, the value to which it converges is not needed.)
If [itex]a_n[/itex] is a sequence of positive terms, then the following conditions are true for the limit:
If lim<1, the series converges.
If lim>1, the series diverges.
If lim=1, inconclusive.
The Attempt at a Solution
By simply plugging values into the formula and rearranging the resulting fractions, I get this form:
From what I can see, applying L'Hopital's rule won't help get this limit into a solvable form, and no algebraic transformations pop out at me as being helpful.
How would one start solving this limit?