Question on limits on factorial

lim(n→∞) [n!/(n+2)!]

how can I solve this? Can someone guides me? Thanks!

(n+2)! = n! * (n+1) * (n+2)

so n!/(n+2)! simplifies to 1/[(n+1)(n+2)]

The denominator approaches ∞ much faster than the numerator does. Because of that, as n approaches ∞ in both cases, the denominator will end up exponentially higher.

When the denominator approaches ∞ more rapidly than the numerator, the limit as n approaches ∞ is 0.

Hint: (n+2)! = (n+2)(n+1)n!