Determine if the sequence is monotonic and if it is bounded.
-$$a _ { n } = \frac { 4 ^ { n } } { 4 n }$$
A) decreasing; unbounded
B) nondecreasing; bounded
C) nondecreasing; unbounded
D) not monotonic; unbounded

Question

Quizplus · Accepted Answer

The sequence $\frac{4^n}{4n}$ is nondecreasing because as $n$ increases, both the numerator $4^n$ and the denominator $4n$ increase, but the numerator grows exponentially while the denominator grows linearly, making the overall fraction increase. It is unbounded because as $n$ approaches infinity, the value of $\frac{4^n}{4n}$ increases without bound due to the exponential growth in the numerator outpacing the linear growth in the denominator.

Determine If the Sequence Is Monotonic and If It Is an=4n4na _ { n } = \frac { 4 ^ { n } } { 4 n }an​=4n4n​

Determine If the Sequence Is Monotonic and If It Is $a _ { n } = \frac { 4 ^ { n } } { 4 n }$