Find the limit of the sequence if it converges; otherwise indicate divergence.
-$$a _ { n } = \sqrt [ n ] { 5 ^ { n } \cdot n }$$
A) 1
B) 5
C) 0
D) Diverges

Question

Quizplus · Accepted Answer

The sequence $\sqrt [ n ] { 5 ^ { n } \cdot n }$ can be rewritten as $(5^n \cdot n)^{1/n}$. This simplifies to $5 \cdot n^{1/n}$. As $n$ approaches infinity, $n^{1/n}$ approaches 1, making the limit of the sequence $5 \cdot 1 = 5$.

Find the Limit of the Sequence If It Converges; Otherwise an=5n⋅nna _ { n } = \sqrt [ n ] { 5 ^ { n } \cdot n }an​=n5n⋅n​

Find the Limit of the Sequence If It Converges; Otherwise $a _ { n } = \sqrt [ n ] { 5 ^ { n } \cdot n }$