Use the Root Test to determine the convergence or divergence of the series
$\sum _ { n = 1 } ^ { \infty } e ^ { 3 n }$
A)converges
B)diverges

Question

Quizplus · Accepted Answer

We apply the Root Test:

\begin{aligned} \lim _ { n ightarrow \infty } \sqrt [ n ] {|e ^ { 3n }|} &= \lim _ { n ightarrow \infty } {|e ^ { 3 }|} \ &= e ^ {3} > 1 \end{aligned}

Since the limit is greater than 1, by the Root Test, the series diverges. Therefore, the best choice is B.

Use the Root Test to Determine the Convergence or Divergence ∑n=1∞e3n\sum _ { n = 1 } ^ { \infty } e ^ { 3 n }∑n=1∞​e3n

Use the Root Test to Determine the Convergence or Divergence $\sum _ { n = 1 } ^ { \infty } e ^ { 3 n }$