Determine if the series converges or diverges.
Even though this really looks like a ratio test series, remember to try the divergence test first.
The formula for the nth term simplifies to
Now we can see that as n goes to infinity, the value of the nth term approaches . Since the terms don't converge to zero, the series diverges.
While we could use the ratio test, it's horrible and messy unless we simplify the terms first. And if we're going to simplify the terms anyway, we may as well use the divergence test.