If \(\frac{(n+1)!}{(n-1)!}=20\), what is the value of (n)?

Correct answer: 4

Using \((n+1)!=(n+1)n(n-1)!\), we obtain \(\frac{(n+1)!}{(n-1)!}=n(n+1)\). Thus, \(n(n+1)=20\). Since the consecutive integers \(4\) and \(5\) have product \(20\), \(n=4\). For option \(5\), the product is \(5\times6=30\), so it is incorrect. Exam tip: In a factorial ratio, expand the larger factorial up to the smaller one and cancel common terms.