Determine the limit of the sequence $a _ { n } = \frac { n ! } { ( n + 3 ) ! }$ .
A)0
B)1
C)2
D) $e$
E)3
F) $\frac { 1 } { 2 }$
G) $\frac { 1 } { 3 }$
H)Divergent

Question

Determine the limit of the sequence $a _ { n } = \frac { n ! } { ( n + 3 ) ! }$ .
A)0
B)1
C)2
D) $e$ 
E)3
F) $\frac { 1 } { 2 }$ 
G) $\frac { 1 } { 3 }$ 
H)Divergent

Quizplus · Accepted Answer

The limit of $a_n = \frac{n!}{(n+3)!}$ simplifies to $\frac{1}{(n+1)(n+2)(n+3)}$ as $n!$ cancels out most of the factorial in the denominator, leaving a fraction that approaches 0 as $n$ approaches infinity.

Determine the Limit of the Sequence an=n!(n+3)!a _ { n } = \frac { n ! } { ( n + 3 ) ! }an​=(n+3)!n!​

Determine the Limit of the Sequence $a _ { n } = \frac { n ! } { ( n + 3 ) ! }$