Determine the convergence of ∑n=1∞nn3nn!\sum_{n=1}^{\infty} \frac{n^n}{3^n n!}∑n=1∞3nn!nn.
Converges because ratio limit is e/3<1e/3 < 1e/3<1
Diverges because ratio limit is e/3>1e/3 > 1e/3>1
Converges because ratio limit is 3/e<13/e < 13/e<1
Diverges because ratio limit is 111