Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = ( 2 + n ) ^ { 1 / n }$$
A) Diverges
B) Converges

Question

Quizplus · Accepted Answer

The sequence $$a _ { n } = ( 2 + n ) ^ { 1 / n }$$ converges as $n$ approaches infinity. As $n$ becomes very large, the term $2$ becomes negligible compared to $n$, and the expression behaves similarly to $n^{1/n}$, which is known to converge to $1$. Therefore, the sequence converges.

Graph the Function Corresponding to the Sequence Defined an=(2+n)1/na _ { n } = ( 2 + n ) ^ { 1 / n }an​=(2+n)1/n

Graph the Function Corresponding to the Sequence Defined $a _ { n } = ( 2 + n ) ^ { 1 / n }$