Before we start calculating the limit, we will simplify the expression for the general term of the sequence. To that end we shall use recursive definition of factorial.

`n! ={(1 if n=0),(n(n-1)! if n>0):}`

`a_n=((n-2)!)/(n!) =((n-2)!)/(n(n-1)(n-2)!)=1/(n(n-1))`

Now it becomes easy to calculate the limit and determine convergence of the sequence.

`lim_(n to infty)a_n=lim_(n to infty)1/(n(n-1))=1/(infty cdot infty)=1/infty=0`

**As we can see the sequence is convergent and its limit is equal to zero.**

The image below shows the first 15 terms of the sequence. We can see they are approaching `x`-axis i.e. the sequence converges to zero.

**Further Reading**