factrial notation

Hiiiiiii.... everyone...its parul...

         today i am going to tell  u about factorial notation....

The symbon n! means to multiply all the positive integers from n consecutively down to 1 

n!=n(n-1)(n-2).........(3) (2) (1), where n is an that element which positive integers. 

exp. 1=

0!=1 it is always defined as 1 

exp.2=

         5!=5 (5-1)(5-2)(5-3)(5-4)(5-5) 

             5*4*3*2*1=120

exp.3 

        11!=  11*10*9*8*7*6!=  279n17600

exp.4=     

       n(n-5)!=24(n-6)!

           n(n-5) ( n-6)!=24 (n-6)!

cancel (n-6)!

           n(n-5)=24

           n*n-5n-24=0

         n*n-8n+3n-24=0

n(n-8)+3(n-8)=0

(n-8) (n+3)=0

n-8=0 or n+3=0

n=8  or n= (-3)

n=-3 reject it bcz n is an elemnt of negative integer....

    

  check ans... put the value of n=8 in eq.

      8(8-5)!=24(8-6)!

     8(3)!=24 (2)! 

     8*3*2*1=24*2*1

48=48

L.H.S=R.H.S

                     so its the easiest way to solve.........the factorial notation