Use the Ratio Test to determine if the series converges or diverges.
-$$\sum _ { n = 1 } ^ { \infty } n ! e ^ { - 7 n }$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

Applying the Ratio Test, we have 
$$\lim _ { n \rightarrow \infty } \left| \frac { a _ { n + 1 } } { a _ { n } } \right| = \lim _ { n \rightarrow \infty } \frac { (n+1)! e ^ { -7(n+1)}} {n! e ^ { -7n} } = \lim _ { n \rightarrow \infty } (n+1) e ^ { -7 } = \infty$$
Since the limit is greater than 1, the series diverges. Therefore, the answer is B.

Use the Ratio Test to Determine If the Series Converges ∑n=1∞n!e−7n\sum _ { n = 1 } ^ { \infty } n ! e ^ { - 7 n }n=1∑∞​n!e−7n

Use the Ratio Test to Determine If the Series Converges $\sum _ { n = 1 } ^ { \infty } n ! e ^ { - 7 n }$