Determine if the sequence is monotonic and if it is bounded.
-$$a _ { n } = 4 - \frac { 1 } { n }$$
A) increasing; bounded
B) not monotonic; bounded
C) decreasing; unbounded
D) nonincreasing; bounded

Question

Quizplus · Accepted Answer

The sequence $a_n = 4 - \frac{1}{n}$ is increasing because as $n$ increases, the value of $\frac{1}{n}$ decreases, making $4 - \frac{1}{n}$ increase. It is bounded because it is always less than 4 (upper bound) and approaches 4 as $n$ goes to infinity, and it has a lower bound (for example, at $n=1$, $a_1 = 3$).

Determine If the Sequence Is Monotonic and If It Is an=4−1na _ { n } = 4 - \frac { 1 } { n }an​=4−n1​

Determine If the Sequence Is Monotonic and If It Is $a _ { n } = 4 - \frac { 1 } { n }$