Question 25279: Evaluate:
1*1!+ 2*2!+3*3!+.....+n*n! where n is in N
I started with if
n=1 then 1*1=1
n=2 then 1*1 +2*2*1=5
n=3 then 1*1 +2*2*1+3*3*2*1=23
............................
...........................
n=n then 1*1 +2*2*1+3*3*2*1+.....+n*n(n-1)(n-2)....3*2*1
the answer is (n+1)!-1 i can drive to this answer would you please help me.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! CONSIDER THE FOLLOWING EQUALITY
(N+1)!-N!=(N+1)*N!-N!=N!*(N+1-1)=N*N!...THAT IS
(N+1)!-N!=N*N!....PUT IN THIS EQUALITY N=1,2,3,....ETC...TILL N AND ADD THEM UP
N=1....WE GET 2!-1!=1*1!
N=2...........3!-2!=2*2!
N=3...........4!-3!=3*3!
........................
.........................
N=N.......(N+1)!-N!=N*N!
-----------------------------ADDING ALLTHE ABOVE,WE GET
..........(N+1)!-1!=1*1!+2*2!+3*3!+...........N*N!............PROVED
|
|
|
