Resolved: factorial properties

Hi, Sheref Morad,

Thanks for reaching out. I understand you're looking for clarity on the factorial property given by the equation (n+1)! = n! * (n+1). Let’s break it down:

1. Factorials: The notation

   • n! (n factorial) is defined as the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

2. Expanding (n+1)!:

   • When we write (n+1)!, we mean (n+1) * n!. Therefore:
     • (n+1)! = (n+1) × n!
   • This conforms to the definition of factorial, which states that for any positive integer n, multiplying (n!) by (n+1) gives us (n+1)!.

So, the equation (n+1)! = n! * (n+1) holds true due to the fundamental definition of what a factorial is.

If this is still unclear or if you have more specific points you want to discuss, please let me know!