Determine if the sequence is monotonic and if it is bounded.
-$$a _ { n } = \frac { 2 ^ { n } } { 2 n }$$
A) decreasing; unbounded
B) nondecreasing; bounded
C) not monotonic; unbounded
D) nondecreasing; unbounded

Question

Quizplus · Accepted Answer

The sequence $a_n = \frac{2^n}{2n}$ is nondecreasing because as $n$ increases, the numerator $2^n$ grows exponentially, while the denominator $2n$ grows linearly, making the overall fraction increase. It is unbounded because there is no limit to how large $2^n$ can grow, even when divided by $2n$, meaning the sequence can grow indefinitely.

Determine If the Sequence Is Monotonic and If It Is an=2n2na _ { n } = \frac { 2 ^ { n } } { 2 n }an​=2n2n​

Determine If the Sequence Is Monotonic and If It Is $a _ { n } = \frac { 2 ^ { n } } { 2 n }$