Determine whether the given series converges or diverges. If it converges, find its sum. $\sum _ { n = 1 } ^ { \infty } \left( 1 + \frac { 8 } { n } \right) ^ { n }$
A) $e ^ { - 8 }$
B) Diverges
C) 1
D) $e ^ { 8 }$

Question

Quizplus · Accepted Answer

The series diverges because the general term $\left( 1 + \frac { 8 } { n } \right) ^ { n }$ approaches $e^8$ as $n$ approaches infinity, which does not tend to zero.

Determine Whether the Given Series Converges or Diverges ∑n=1∞(1+8n)n\sum _ { n = 1 } ^ { \infty } \left( 1 + \frac { 8 } { n } \right) ^ { n }∑n=1∞​(1+n8​)n

Determine Whether the Given Series Converges or Diverges $\sum _ { n = 1 } ^ { \infty } \left( 1 + \frac { 8 } { n } \right) ^ { n }$