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## Homework Statement

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.)

[tex]\sum_{n=1}^{\infty}\frac{n}{(e^n)^2}[/tex]

## Homework Equations

Ratio Test:

If [itex]a_n[/itex] is a sequence of positive terms, then the following conditions are true for the limit:

[tex]\lim_{n\to\infty}\frac{a_{n+1}}{a_n}[/tex]

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:

[tex]\frac{(e^n)^2(n+1)}{(e^{(n+1)})^2\cdot n}[/tex]

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?

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