Determine if this series is convergent/divergent using the ratio test.

(2n-1)! / 3^(n+1)

Starting at n = 1 and going to infinity. Thanks in advance.

For the ratio test, look at the limit of the ratio of |a[n+1] / a[n]|, as n goes to infinity. If the limit is >1, then the series diverges (obviously, because the individual terms keep getting bigger). If the limit is <1, it converges, and if the limit is 1, the test is inconclusive and you need to try something else :)

Let's look at the first few terms of this sequence:
1/9
6/27
120/81
5040/243
It's pretty obvious that the ratio is growing (I'll leave that for you to prove properly) and so the series will grow to infinity.

congergent

Lim (2n-1)! / 3^(n+1) = ∞
n→ ∞