Does ∑n=1∞2nn!nn\sum_{n=1}^{\infty} \frac{2^n n!}{n^n}∑n=1∞nn2nn! converge?
Converges because 2/e<12/e < 12/e<1
Diverges because 2/e>12/e > 12/e>1
Converges because 2/e>12/e > 12/e>1
Inconclusive