BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Sum of the fractions

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

Sum of the fractions

by gmattesttaker2 » Sat May 03, 2014 10:42 am
Hello,

Can you please tell me how to solve this:


What is 1/(1)(2) + 1/(2)(3) + 1/(3)(4) + 1/(4)(5) + 1/(5)(6) + 1/(6)(7) + 1/(7)(8) + 1/(8)(9) + 1/(9)(10) ?


OA: [spoiler]9/10 [/spoiler]


Thanks a lot,
Sri
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Sat Mar 15, 2014 10:36 pm
Thanked: 1 times

by raj44 » Sat May 03, 2014 11:24 pm
Hi,

This can be solved like :

1. Determine the nth term of the series which happens to be 1/(n)(n+1) where 1<= n <= 9

2. Now we can employ partial fraction skills to separate the multiplying denominators and determine the Numerator coefficients:

therefore, the exp 1/(n)(n+1)= 1/n-1/n+1 where 1<= n <= 9.

This is called a telescoping series. write out the first few terms of each of these two series:

1/n: 1, 1/2, 1/3, 1/4, 1/5, ...

-1/(n+1): -1/2, -1/3, -1/4, -1/5, -1/6, ...

Add these together and you should notice that almost everything cancels except for a 1 at the beginning of the 1/n series and a term at the end of the -1/(n+1) series.

Therefore we have 1-0.1=0.9= 9/10 as the answer.

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:


What is 1/(1)(2) + 1/(2)(3) + 1/(3)(4) + 1/(4)(5) + 1/(5)(6) + 1/(6)(7) + 1/(7)(8) + 1/(8)(9) + 1/(9)(10) ?


OA: [spoiler]9/10 [/spoiler]


Thanks a lot,
Sri
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sun May 04, 2014 12:03 am
Hi Sri,

What was the original question (and answers) that this concept was a part of?

In many cases, a Quant question that looks like it requires "lots of math" is actually based on a pattern that will allow you to avoid most of that math. Sometimes the answers are written in such a way that you can also avoid most of the math.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun May 04, 2014 2:21 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:


What is 1/(1)(2) + 1/(2)(3) + 1/(3)(4) + 1/(4)(5) + 1/(5)(6) + 1/(6)(7) + 1/(7)(8) + 1/(8)(9) + 1/(9)(10) ?


OA: [spoiler]9/10 [/spoiler]


Thanks a lot,
Sri
If x = 1/2 + 1/6 + 1/12 + 1/20 + ... + 1/90, what is the value of x?
WRITE IT OUT and LOOK FOR A PATTERN.

Sum of the first 2 terms:
1/2 + 1/6 = 2/3.

Sum of the first 3 terms:
2/3 + 1/12 = 3/4.

Sum of the first 4 terms:
3/4 + 1/20 = 4/5.

In each case:
The NUMERATOR of the sum = the NUMBER OF TERMS.
THE DENOMINATOR of the sum = NUMERATOR + 1.

Thus:
x = sum of the first 9 terms = [spoiler]9/10[/spoiler].
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

by gmattesttaker2 » Mon May 05, 2014 5:49 pm
GMATGuruNY wrote:
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:


What is 1/(1)(2) + 1/(2)(3) + 1/(3)(4) + 1/(4)(5) + 1/(5)(6) + 1/(6)(7) + 1/(7)(8) + 1/(8)(9) + 1/(9)(10) ?


OA: [spoiler]9/10 [/spoiler]


Thanks a lot,
Sri
If x = 1/2 + 1/6 + 1/12 + 1/20 + ... + 1/90, what is the value of x?
WRITE IT OUT and LOOK FOR A PATTERN.

Sum of the first 2 terms:
1/2 + 1/6 = 2/3.

Sum of the first 3 terms:
2/3 + 1/12 = 3/4.

Sum of the first 4 terms:
3/4 + 1/20 = 4/5.

In each case:
The NUMERATOR of the sum = the NUMBER OF TERMS.
THE DENOMINATOR of the sum = NUMERATOR + 1.

Thus:
x = sum of the first 9 terms = [spoiler]9/10[/spoiler].
Hello Mitch,

Thanks a lot for the detailed solution.

Best Regards,
Sri
Top
Post new topic Post Reply
• Page 1 of 1