(Solved): Use the Root Test to determine whether the series convergent or divergent. ...

Use the Root Test to determine whether the series convergent or divergent.

?	?5n n + 1   3n
n = 1

 

Evaluate the following limit.

 lim n ? ? 

n

|an|

 

Since \( \lim _{n \rightarrow \infty}\left|\frac{a_{n}+1}{a_{n}}\right| \geq 1 \) Need Help? [3/4 Points] SCALCET9M 11.6.C Use the Root Test to determine whether the series convergent or divergent: \[ \sum_{n=1}^{\infty}\left(\frac{-5 n}{n+1}\right)^{3 n} \] Identify \( a_{n} \). \[ 5^{3 n}\left(-\frac{n}{n+1}\right) 3 n \] Evaluate the following limit. \[ \lim _{n \rightarrow \infty} \sqrt[n]{\left|a_{n}\right|} \] \[ \frac{1}{\left(1+\frac{1}{n}\right)^{125}} \] Since \( \lim _{n \rightarrow \infty} \sqrt[n]{\left|a_{n}\right|}, 1 \) 1anstidy on Codice:u itha 4vasining fint. \[ \begin{array}{l} \lim _{n \rightarrow i} \sqrt[t]{||_{a} \mid} \\ \frac{1}{1 \mathrm{k}-\frac{\mathrm{t}}{\mathrm{m}} / 1 \mathrm{t}} \\ \text { Binde } \operatorname{len}_{x \rightarrow \infty}+\sqrt{\mid t_{+}} \quad \text { of } \\ \end{array} \]