Difficult Math Problem #97 - Algebra - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Difficult Math Problem #97 - Algebra

Expert replies

800guy: Master | Next Rank: 500 Posts; Posts: 354; Joined: Tue Jun 27, 2006 9:20 pmFollowed by: 5 members; Thanked: 11 times

by 800guy » Wed Feb 14, 2007 3:11 pm

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) None of these

oa coming when some people answer/explain. from diff math doc.

Like this post

Source: Beat The GMAT — Problem Solving | Wed Feb 14, 2007 3:11 pm

kandelaki: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Feb 05, 2007 12:35 am

by kandelaki » Thu Feb 15, 2007 3:27 am

Sn = n ( 2a1 + (n - 1)d ) / 2

so Sn= n( 2*1.1!+(n-1)*1.1!)/2 =n(2*1.1!+1.1n!-1.1!)/2=n1.1!(2+n-1)/2=

=1.1n!(n+1)/2

i can not go any further...

Like this post

banona: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sat Dec 30, 2006 7:46 pm; Thanked: 1 times

by banona » Thu Feb 15, 2007 6:39 am

Here is my attempt to solve this difficlt problem:

we are looking for the sum ( kK!) as K from 2 to n.
First , we can easily eliminate first and second choices, because the first one ( n!+1) is vritually too small to be the sum we are looking for;
The second choice ( n+1)! is even; and the sum we are looking for is odd;
Now choices are narrowed to the three choices that countain the expression ( n+1)!

Let's examine the following difference :
(n+1)! - [ 1*1! + 2*2! +........+ n *n! )] = (n+1)*n! - [ 1*1! + 2*2! +........+ n *n! )] = n! - [ 1*1! + 2*2! +........+ (n-1) *(n-1)! )] = n ( n-1)! - [ 1*1! + 2*2! +........+ (n-1) *(n-1)! )] = (n-1)(n-2)! - [ 1*1! + 2*2! +........+ (n-2) *(n-2)! )]
THE GENERAL FORMULA, when doing so (k) times, is
(n-K+1)(n-K)! - [ 1*1! + .......+ (n-k) *(n-K)! )]

Therfore at the end ; k is (n-1), so the sum becomes :
2*(1)! - [ 1*1!] = 1 = (n+1)! - [ 1*1! + 2*2! +........+ n *n! )] = 1
So,
[ 1*1! + 2*2! +........+ n *n! )] = (n+1)! -1

I hope I am not abusively simplifying things,
please, any comment !!!!!

Like this post

banona: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sat Dec 30, 2006 7:46 pm; Thanked: 1 times

by banona » Thu Feb 15, 2007 7:06 am

Hy Kandelaki,
I wonder if you can use this general formula like :
Sn = n ( 2a1 + (n - 1)d ) / 2
I think it's only valid when adding consecutive numbers, like (1, 2,3,......n) or when numbers are equally far from each other; like consecutive evens ( 2; 4; 6; ......2n) or consecutives odds;
However, in our case 11! ; 22! ; 33!; ....... nn! are not consecutive numbers;

Can Mathematics tutors comment ?

Like this post

800guy: Master | Next Rank: 500 Posts; Posts: 354; Joined: Tue Jun 27, 2006 9:20 pmFollowed by: 5 members; Thanked: 11 times

by 800guy » Fri Feb 16, 2007 11:27 am

oa:

1.1! + 2.2! + 3.3! + ......+n.n!
=1.1! + (3-1)2! + (4-1)3! +......+ ((n+1)-1) n!
=1.1!+3!-2!+4!-3!+.......+(n+1)!-n!

So it is (n+1)! -1 (Answer choice 4)

Like this post

gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

Re: Another approach

by gabriel » Sun Feb 18, 2007 4:31 am

Mark Dabral wrote:hi guys,

i am sure you know that this question is really way out of GMAT league.

S = 1(1!) + 2(2!) + 3(3!) + 4(4!) + ..... + (n-1)[(n-1)!] + n(n!)

S = [2-1](1!) + [3-1](2!) + [4-1](3!) + [5-1](4!) + ..... + (n-1)[(n-1)!] + [n+1 - 1](n!)

S = 2(1!) - 1! + 3(2!) - 2! + 4(3!) - 3! + 5(4!) - 4!+ ..... + n[(n-1)!] - (n-1)! + (n+1)(n!) - n!

S = 2! - 1! + 3! - 2! + 4! - 3! + 5! - 4!+ ..... + n! - (n-1)! + (n+1)! - n!

The terms 2!, 3!, 4!, and so on cancel out leaving only (n+1)! and the 1 term.

Therefore, S = (n+1)! - 1

Cheers,
Mark

hi there, great effort..... but u know what such q are much more easier than they seem..... make use of the answer choices...

in this particular q all that has to be done is choose a value for n .... eg let
n=2 so the series will be 1*1!+ 2*2! = 5.... now substitute n=2 in the answer choices... and u will find that only ( n+1 ) ! - 1 will give u a value 5 for n=2..... hope that helps

Like this post

gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

by gabriel » Sun Feb 18, 2007 4:35 am

banona wrote:Hy Kandelaki,
I wonder if you can use this general formula like :
Sn = n ( 2a1 + (n - 1)d ) / 2
I think it's only valid when adding consecutive numbers, like (1, 2,3,......n) or when numbers are equally far from each other; like consecutive evens ( 2; 4; 6; ......2n) or consecutives odds;
However, in our case 11! ; 22! ; 33!; ....... nn! are not consecutive numbers;

Can Mathematics tutors comment ?[/quote

yup....u r rite.... that is the formula for a AP...ie for a series with equally spaced elements...the formula cant be used in this case

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review