What is the value of \(\frac{(n+1)!}{(n+1)n!}\)?

Correct answer: \(1\)

Using the factorial identity, \((n+1)!=(n+1)\times n!\). Therefore, the numerator and denominator are equal, so \(\frac{(n+1)!}{(n+1)n!}=1\). \(n+1\) is not the answer because it is only one factor in the expanded numerator; \(n!\) is also present in the denominator. Exam tip: In factorial fractions, first expand the larger factorial in terms of the smaller one and then cancel common factors.