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

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Senior Manager
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Find the value of 1.1! + 2.2! + 3.3! + ......+n.n! (1) [#permalink]

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09 Nov 2003, 05:15
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Difficulty:

(N/A)

Question Stats:

83% (00:04) correct 17% (00:00) wrong based on 5 sessions

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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
(5) n! + 3

hint: one extremely short and simple way

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09 Nov 2003, 16:30
choice 3 is right... is there any other way to solve... which short way you're talking about vicky??
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shubhangi

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09 Nov 2003, 17:31
How exactly do you calculate factorial of decimals? Isn't factorial only calculated from integers?!?

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09 Nov 2003, 18:22
OOOPS. I did not even think that it was decimal. I thought it was multiplication. I thought the question in the following way.

1*1! + 2*2! + 3*3! + ....... + n*n!

Vicki,

Is my interpretation of the question correct? Please let us know.

Thanks

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Senior Manager
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09 Nov 2003, 20:42
thats correct. It is the multiplication of numbers...
thanks

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SVP
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11 Nov 2003, 00:38
consider n=2

1*1!+2*2!=1+4=5

check options

A=3 out
B=3!=6 out
C=6-1=5 OK
D=6+1=7 out
E=2+3=5 OK

consider n=3; S=5+18=23
C=23 OK
E=6+3=9 out

So, C.

Any other approach.

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20 Nov 2003, 06:08
Vicky wrote:
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
(5) n! + 3

hint: one extremely short and simple way

You can solve this easily using substitution, but that's no fun.

Let's see if we can manipulate all of the a*a! terms

a*a! = (a+1 - 1)*a! = (a+1)a! - a! = (a+1)! - a!

Hence, 1*1! + 2*2! + .... +n*n! = (2!-1!) + (3! - 2!) + .....(n + 1)! - n!.

If you add up all of the terms, you get: -1! + (n+1)! or

(n+1)! - 1

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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Re: PS: n!   [#permalink] 20 Nov 2003, 06:08
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