Questions: Simplifique a expressão (n-2)!/n!, com n>2; n ∈ N.

Solution Steps

To simplify the expression \(\frac{(n-2)!}{n!}\), we can use the property of factorials. Recall that \(n! = n \cdot (n-1) \cdot (n-2)!\). Using this property, we can rewrite the expression and simplify it.

We start with the given expression: \[ \frac{(n-2)!}{n!} \]

Recall the property of factorials: \[ n! = n \cdot (n-1) \cdot (n-2)! \] Using this property, we can rewrite the denominator: \[ n! = n \cdot (n-1) \cdot (n-2)! \]

Substitute the expanded form of \(n!\) into the original expression: \[ \frac{(n-2)!}{n \cdot (n-1) \cdot (n-2)!} \] Cancel out \((n-2)!\) from the numerator and the denominator: \[ \frac{1}{n \cdot (n-1)} \]

Final Answer