Question 25279
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!
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N=N.......(N+1)!-N!=N*N!
-----------------------------ADDING ALLTHE ABOVE,WE GET 
..........(N+1)!-1!=1*1!+2*2!+3*3!+...........N*N!............PROVED