Determine if the sequence is monotonic and if it is bounded.
-$$a _ { n } = \frac { 3 n + 1 } { n + 1 }$$
A) not monotonic; bounded
B) nondecreasing; bounded
C) decreasing; bounded
D) decreasing; unbounded

Question

Quizplus · Accepted Answer

The sequence is nondecreasing because as $n$ increases, the value of $a_n$ increases or remains constant. This can be shown by comparing $a_n$ and $a_{n+1}$ and noting that $a_{n+1}$ is always greater than or equal to $a_n$. The sequence is bounded because it approaches 3 as $n$ goes to infinity, meaning it will never exceed 3 but will get arbitrarily close to it.

Determine If the Sequence Is Monotonic and If It Is an=3n+1n+1a _ { n } = \frac { 3 n + 1 } { n + 1 }an​=n+13n+1​

Determine If the Sequence Is Monotonic and If It Is $a _ { n } = \frac { 3 n + 1 } { n + 1 }$