Find the limit of the sequence if it converges; otherwise indicate divergence.
-$$a _ { n } = \left( \frac { 9 } { n } \right) ^ { 9 / n }$$
A) 1
B) ln 9
C) 0
D) Diverges

Question

Quizplus · Accepted Answer

The limit of the sequence $\left( \frac { 9 } { n } \right) ^ { 9 / n }$ as $n$ approaches infinity is 1. This is because the base $\frac{9}{n}$ approaches 0 and the exponent $\frac{9}{n}$ approaches infinity, but the overall expression approaches the form of $1^\infty$, which is a special case leading to the limit being 1.

Find the Limit of the Sequence If It Converges; Otherwise an=(9n)9/na _ { n } = \left( \frac { 9 } { n } \right) ^ { 9 / n }an​=(n9​)9/n

Find the Limit of the Sequence If It Converges; Otherwise $a _ { n } = \left( \frac { 9 } { n } \right) ^ { 9 / n }$