Determine whether the series converges conditionally, absolutely, or not at all.
The ratio test looks at the absolute value of the ratio between terms:
This is the same thing as the ratio between the absolute values of the terms:
This means when we use the ratio test, we're really checking the convergence of the series
If the ratio test says "yes, the series converges" it actually means "yes, the original series converges absolutely."
For this particular series, we look at
Since the limit is less than 1, the series converges. Since we were really looking at the terms of , the original series converges absolutely.