Answer:
To verify that [n+3]! / n! = (n+1), we can use the definition of factorial:
[n+3]! = (n+3) * (n+2) * (n+1) * n!
And we can cancel out n! from both sides of the equation:
(n+3) * (n+2) * (n+1) = n+1
Which is true, and thus [n+3]! / n! = (n+1) holds true.
Another way to verify this is by simplifying the RHS and LHS
(n+1) = (n+1)
And the LHS,
(n+3)! = (n+3)(n+2)(n+1)n! = (n+1)(n+2)(n+3)n! = (n+1)(n+2)(n+3)!/n!
which is also equal to (n+1)
So, [n+3]! / n! = (n+1) is true.