I am back to my blog guys!!!! Let's start with Why the factorial of 0(0!) is 1?

Explanation :

If you did mathematics related to factorials then you saw that 0! = 1 and without any question took it for granted because your teacher may be told you that it's just a formula,probably they did not tell you what's the logic behind it.

But the truth is there’s a logic behind it and that is hidden inside the rules of the factorial itself.Let's explore it.

The formula of factorial of n is -

n! = 1*2*3*.......*(n-3)*(n-2)*(n-1)*n      where n>0   ……………...(i)

Now let's take some examples  -

8! = 8*7*6*5*4*3*2*1

7! = 7*6*5*4*3*2*1 = 8!/8

6! = 6*5*4*3*2*1 = 7!/7

………… so on.

I think you started to notice a predictable pattern and we can define the pattern mathematically -

n! = (n+1)! / (n+1)     where n ≥0   ……………...(ii)

Now use the above formula from (ii) which we got by observing the pattern to calculate 0!  -

0! = (0+1)!/(0+1) = 1!/1 = 1
It's not magic,it's a logic,Waoooo!!!!!!

Remember without the (ii) you can calculate the factorial of 0 if you got the logical pattern. That’s it.Now you know why 0! = 1,you don’t need to memorize it.Yeeeeaaaah!!!!!!!!!

If you want to know more about factorial click this link- Factorial_Wiki

If you have any questions feel free to ask.

Thank You☺️