GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 26 May 2019, 11:11

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42
GPA: 3.82
If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

Show Tags

New post 14 Sep 2018, 00:42
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:20) correct 22% (02:39) wrong based on 50 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

If \(\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},\) then what is the value of \(\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}\)

\(A. \frac{1}{100}\)
\(B. \frac{1}{50}\)
\(C. \frac{49}{50}\)
\(D. \frac{99}{100}\)
\(E. \frac{1}{2}\)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7688
Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

Show Tags

New post 14 Sep 2018, 01:55
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},\) then what is the value of \(\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}\)

\(A. \frac{1}{100}\)
\(B. \frac{1}{50}\)
\(C. \frac{49}{50}\)
\(D. \frac{99}{100}\)
\(E. \frac{1}{2}\)



If \(\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},\) ....
So 1/(1*2)=1/1-1/2...
1/(2*3)=1/2-1/3..
So sum = 1-1/2+1/2-1/3......-1/99+1/99-1/100=1-1/100=99/100

D
_________________
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3728
Location: Canada
Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

Show Tags

New post 14 Sep 2018, 06:54
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(\frac{1}{n(n+1)} = \frac{1}{n} – \frac{1}{(n+1)},\) then what is the value of \(\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}\)

\(A. \frac{1}{100}\)
\(B. \frac{1}{50}\)
\(C. \frac{49}{50}\)
\(D. \frac{99}{100}\)
\(E. \frac{1}{2}\)


If 1/n(n+1) = 1/n – 1/(n+1), then...

1/(1*2) = 1/1 - 1/2
1/(2*3) = 1/2 - 1/3
1/(3*4) = 1/3 - 1/4
.
.
.
1/(98*99) = 1/98 - 1/99
1/(99*100) = 1/99 - 1/100

So, 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100) = (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + . . . (1/98 - 1/99) + (1/99 - 1/100)
= 1/1 - 1/100
= 99/100

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*  [#permalink]

Show Tags

New post 16 Sep 2018, 18:34
=>
\(\frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + … + \frac{1}{(99*100)}
= (\frac{1}{1} – \frac{1}{2}) + (\frac{1}{2} – \frac{1}{3}) + (\frac{1}{3} – \frac{1}{4}) + … + (\frac{1}{99} – \frac{1}{100}) = \frac{1}{1} – \frac{1}{100} = 1 – \frac{1}{100} = \frac{99}{100}\) after cancellation of the inner terms.

Therefore, the answer is D.
Answer: D
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*   [#permalink] 16 Sep 2018, 18:34
Display posts from previous: Sort by

If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.