Is this the series?
In any case, note that this is equivalent to:
by simple exponent rules. We can see this is a sum of two geometric series ( ) which of course converges.
There are two different questions but I am hoping that if I get help with the first one, I will be able to do the second one on my own.
Find the sum of the series if it converges or show that it diverges
∑ n=0 to infinity of [2^(3n)-1] / [ 3^(2n)]
Do I do the nth term test and take the limit of it? I am not good at limits either.