A note on the Factorial Function

Write down 0,1,2,3,4,5 and  put parallely square of each number like 0,1,4,9,16,25, then start to subtract the bigger one to the lower one (1--0),(4--1),(9--4),(16--9) and (25--16) to get 1,3,5,7,9 and again subtract the bigger one to the lower one (3--1),(5--3),(7--5) and (9--7) to get (2,2,2,2).
Again we squared each number, at the same time we cubed each number (0,1,8,27,64,125,216) and the  same procedure follows, subtract the bigger one to the lower one (1--0),(8--1),(27--8),(64--27) ,(125--64) and(216--125) to get (1,7,19,37,61,91) and again (7--1),(19--7),(37--19),(61--37) and (91--61), to get (6,12,18,24,30) same again(12--6),(18--12),24--18) and (30--24)  till the result come out here we get (6,6,6,6).
At the same time if we do it again for 4 and 5 (power).When we get 2 for 2 ,6 for 3 ,24 for 4 and 120 for 5. The result is the factorial function.
factorial2
About the author: Piyush Goel is a Diploma Mechanical Engineering passed in the year 1987, Diploma in Material Management, Diploma in Vastu Shastra and Diploma in Business Management. He is very much fond of Mathematics, and is an avid writer of "Mirror Imaged Books" and is featured in the Limca Book of Records, 2012.
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