Question
Download Solution PDFThe value of \(\rm \dfrac{n!(n-1)!}{(n+1)!}\) is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- The factorial (n!) is defined as the product of first n natural numbers.
- n! = n × (n - 1) × (n - 2) × … × 2 × 1.
Calculation:
We know that (n + 1)! = (n + 1) × n × (n - 1) × (n - 2) × ... × 2 × 1 = (n + 1) × n!.
\(\rm \therefore \dfrac{n!(n-1)!}{(n+1)!}=\dfrac{n!\times (n-1)!}{(n+1)\times n!}=\dfrac{(n-1)!}{n+1}\).
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