Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = \left( \frac { 1 } { 20 } + n \right) ^ { 1 / n }$$
A)Converges
B) Diverges

Question

Quizplus · Accepted Answer

The sequence $\left( \frac { 1 } { 20 } + n \right) ^ { 1 / n }$ converges as $n$ approaches infinity. This is because the base of the power, $\frac { 1 } { 20 } + n$, grows without bound, but the exponent, $1/n$, approaches 0. As $n$ becomes very large, the expression $\left( \frac { 1 } { 20 } + n \right) ^ { 1 / n }$ approaches $1^0$, which is 1. Therefore, the sequence converges to 1.

Graph the Function Corresponding to the Sequence Defined an=(120+n)1/na _ { n } = \left( \frac { 1 } { 20 } + n \right) ^ { 1 / n }an​=(201​+n)1/n

Graph the Function Corresponding to the Sequence Defined $a _ { n } = \left( \frac { 1 } { 20 } + n \right) ^ { 1 / n }$