# Determine whether this series converges absolutely, converges conditionally, or diverges. Justify...

## Question:

Determine whether this series converges absolutely, converges conditionally, or diverges. Justify your answer.

{eq}\sum_{n=1}^{\infty} (-1)^{n-1} \frac{(n+2)3^n}{2^{2n+1}} {/eq}

## The Ratio Test:

By the ratio test, if the absolute value of the ratio of the successive terms of a series converges to a limit smaller than one, then the series is absolutely convergent.

## Answer and Explanation:

We use the ratio test to check the convergence of the given series. We calculate the ratio in the ratio test:

{eq}\begin{align} \displaystyle L &=...

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