Determine whether the following series converge or diverge:

(3n^4+6n^2-17)/(2n^6-9n^4+n+1). I compared it with (5/6)^n, which converges

5^n/n!. Converges by ratio test

1/l(og(n))^n converges by ratio test

(-1)^n/n^(1/3) converges by alternating series test since 1/n^(1/3) is a decreasing sequence which tends to 0

I'm a bit suspicious of my answers since I got that they all converge

Thanks in advance