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What is the value of 1*1! + 2*2! + 3!*3! + ............

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What is the value of 1*1! + 2*2! + 3!*3! + ............ [#permalink]

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New post 29 Oct 2005, 10:09
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A
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D
E

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What is the value of 1*1! + 2*2! + 3!*3! + ............ n*n!,
where n! means n factorial or n(n-1)(n-2)...1

(1) n(n-1)(n-1)!
(2) (n+1)!/(n(n-1))
(3) (n+1)! - n!
(4) (n + 1)! - 1!
(5) n!(n-1)
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New post 29 Oct 2005, 13:39
Substituting 3 for n we get the option D as the correct answer.
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Re: PS: P/C Ascent 5/02 [#permalink]

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New post 29 Oct 2005, 19:48
GMATT73 wrote:
What is the value of 1*1! + 2*2! + 3!*3! + ............ n*n!,
where n! means n factorial or n(n-1)(n-2)...1

(1) n(n-1)(n-1)!
(2) (n+1)!/(n(n-1))
(3) (n+1)! - n!
(4) (n + 1)! - 1!
(5) n!(n-1)


1*1!+2*2!+3*3!+......+n*n!
= (2-1)*1! + (3-1)*2! + (4-1)*3! + ...+ [(n+1)-1]*n!
=(2*1! - 1!) + (3*2! - 2!) + ( 4*3! - 3!)+ ......+ [(n+1)*n! - n!]
= 2! - 1! + 3! - 2! + 4!- 3! + ......+ (n+1)! - n!
= -(1!) + (2!- 2!) + (3!-3!) + ( 4!-4!) + .....+ (n!-n!) + (n+1)!
= -(1!) + 0 + 0 + 0 + + 0 + (n+1)!
= (n+1)! - 1!
D it is!
Re: PS: P/C Ascent 5/02   [#permalink] 29 Oct 2005, 19:48
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