Please check whether I did it correctly.

Define if the series is convergent or divergent.
Infinite series (n=1) 1/(square root of (3n-1)
We can use comparison test.
Series to compare to is 1/sguare root of (3n). It is divergent because p=1/2, which is less than1, so it means that the original series is divergent too as a(n) is greate than b(n)
Or we can use the limit comparison test. limit of a(n)/b(n) = 1, which means that both series diverge based on b(n).

Thank you very much. Does this make sense.

2. Yes, that is quite correct.