Which of the following statements about factorials is true for every positive integer \(n\)?

Correct answer: \((n+1)!=(n+1)\cdot n!\)

By definition, \((n+1)!=(n+1)\cdot n!\). Indeed, \((n+1)!=(n+1)\cdot n\cdot(n-1)\cdots1\), while \(n!=n\cdot(n-1)\cdots1\). Therefore, option A is correct. Option B wrongly uses addition; factorials are related through multiplication. Exam tip: to simplify factorial expressions, separate the greatest factor from the larger factorial.