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# Find the value of 1.1! + 2.2! + 3.3! + ......+n.n! 1) n!

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CEO
Joined: 15 Aug 2003
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Find the value of 1.1! + 2.2! + 3.3! + ......+n.n! 1) n! [#permalink]  07 Oct 2003, 15:50
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Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!

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

VP
Joined: 21 Sep 2003
Posts: 1065
Location: USA
Followers: 3

Kudos [?]: 39 [0], given: 0

Let me try...

n.n! = (n+1-1).n! = (n+1).n! - n! = (n+1)! - n!

So the series
1.1! + 2.2! + 3.3! + 4.4! +..............+ n.n!
can be written as :
(2!-1!) + (3! -2!) + (4! - 3!) + ......... + (n+1)! -n!

Cancelling the intermidiate terms we get

-1! + (n+1)! = (n+1)! -1

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