Determine whether series converges or diverges

What test do I use to figure out whether these series converge or diverge?

1) (3+sin(n))/nsqrt(n)

2) (n+1)^3/n!

1) Comparison Test:
(3 + sin n)/(n sqrt(n)) ≤ (3 + 1)/n^(3/2) = 4/n^(3/2).

Since Σ 4/n^(3/2) converges (multiple of a convergent p-series), the series in question also converges.

2) Ratio Test:
r = lim(n→∞) [(n+2)^3/(n+1)!] / [(n+1)^3/n!]
= lim(n→∞) (n+1)^2 / (n+2)^3
= 0 < 1.

So, this series converges.

I hope this helps!