Series Trouble / Diverging Does anyone mind explaining both of these questions, I’m stuck.



*Determine whether the sequence converges or diverges. If it converges, find the limit it converges to. $$\left\lbrace\sqrt[n]{2^{1 + 2n}}\right\rbrace_{n = 1}^\infty$$


*Find the general $n^{th}$ term of the sequence. Then determine whether the sequence converges or diverges. If it converges, find the limit it converges to. $$\left\lbrace 1, \frac42, \frac96, \frac{16}{24}, \frac{25}{120}, \cdots\right\rbrace$$


The second one (problem 4) seems to be $u_n = \frac{n^2}{n!}$ and as $$0 \le u_n \le \frac{n}{n-1}\frac{1}{n-2} \le \frac{4}{n}$$
for $n \ge 4$, it converges to zero. 
