Determine if the sequence is monotonic and if it is bounded.
-$$a _ { n } = \frac { ( n + 7 ) ! } { ( 7 n + 1 ) ! }$$
A) increasing; unbounded
B) not monotonic; bounded
C) decreasing; bounded
D) nondecreasing; bounded

Question

Quizplus · Accepted Answer

The sequence is decreasing because as $n$ increases, the denominator of the fraction grows much faster than the numerator, making each subsequent term smaller than the previous one. It is bounded below by 0 because factorials are always positive, so the sequence can never become negative, and it approaches 0 as $n$ increases.

Determine If the Sequence Is Monotonic and If It Is an=(n+7)!(7n+1)!a _ { n } = \frac { ( n + 7 ) ! } { ( 7 n + 1 ) ! }an​=(7n+1)!(n+7)!​

Determine If the Sequence Is Monotonic and If It Is $a _ { n } = \frac { ( n + 7 ) ! } { ( 7 n + 1 ) ! }$