Deter whether the series converges or diverges....?

Question

Determine whether or not the series converges or diverges. Any test is accepted.

1. &sum (infinity on top; n=1 on bottom) times (3^(2n)/n!)

2. ∑ (infinity on top; n=1 on bottom) times (1/(2+5^n))

3. ∑ (infinity on top; n=1 on bottom) times (3n^3/2n+1)^n

4. ∑ (infinity on top; n=1 on bottom) times (1/(2 sqrt(n)).

Answer 1

1. Diverges. Each new term is 9/n. This is greater than 1/n, which diverges.
2. Converges. Can be shown to have a limiting value.
3. Think this is messed up.
4. Diverges. Terms are greater than 1/n, which diverges.