For the series ∑n=1∞(2n3n+1)n\sum_{n=1}^{\infty} \left(\frac{2n}{3n+1}\right)^n∑n=1∞(3n+12n)n, compute lim supn→∞ann\limsup_{n \to \infty} \sqrt[n]{a_n}limsupn→∞nan.
000
23\frac{2}{3}32
111
∞\infty∞