Apply the Root Test to ∑n=1∞(lnnn)n\sum_{n=1}^{\infty} \left(\frac{\ln n}{n}\right)^n∑n=1∞(nlnn)n
limn→∞ann=∞\lim_{n \to \infty} \sqrt[n]{a_n} = \inftylimn→∞nan=∞; series diverges
limn→∞ann=1\lim_{n \to \infty} \sqrt[n]{a_n} = 1limn→∞nan=1; test is inconclusive
limn→∞ann=0\lim_{n \to \infty} \sqrt[n]{a_n} = 0limn→∞nan=0; series converges
limn→∞ann=e\lim_{n \to \infty} \sqrt[n]{a_n} = elimn→∞nan=e; series diverges