Determine if the series diverge or converge?

Question

So I was wondering what is the best TEST(divergent test, alternating series,power series,ratio test or root test) that we can use for the following series :

Answer 1

Just simplify to $(\frac{3}{8})^n$ and it becomes much easier.

Answer 2

Actually I used the geometric series as noted in this website : Pauls Online Notes

Thank you guys anyway for such a fast response!