SOLUTION: Conjecture a formula for the following sum 1(1!)+2(2!)+3(3!)+....+n(n!).

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Question 28614: Conjecture a formula for the following sum 1(1!)+2(2!)+3(3!)+....+n(n!).
Answer by venugopalramana(3286) About Me  (Show Source):
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Conjecture a formula for the following sum 1(1!)+2(2!)+3(3!)+...+n(n!).
CONSIDER THE EQN.
(N+1)!-N! = N!*(N+1-1)=N*N!
NOW PUT N=1,2,3.... ETC..TILL N IN THIS EQN.AND ADD UP.,WE GET
FOR N=1.......2!-1! = 1*1!
N=2...........3!-2! = 2*2!
N=3...........4!-3! = 3*3!
..........................ETC
N=N........(N+1)!-N!=N*N!
-----------------------------ADD ALL
...........(N+1)!-1!=1*1!+2*2!+3*3!+.........+N*N!
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