I am a beginner in math I was developing a coding problem and here is the pattern which I found: Help me understand the pattern.
Factorial of n will be the sum of all the product of all permutation of digits(1,n-1) taken from 1 to n-1 at a time, with the addition of 1.
I may not sound clear but below is the example. For Example:
factorial 4: numbers = 1,2,3 factorial 4 = [(1)+(2)+(3)]+[(1x2)+(1x3)+(2X3)]+[(1x2x3)] = 23+1 factorial 5: numbers = 1,2,3,4 factorial 5 = [(1)+(2)+(3)+(4)]+[(1x2)+(1x2)+(1X3)+(1x4)+(2+3)+(2+4)+(3+4)]+[(1x2x3)+(1x2x4)+(1x3x4)+(2x3x4)]+[(1x2x3x4)] = 119+1
Can we prove this mathematically?