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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote If 1/n(n+1) = 1/n - 1/(n+1), then what is the value of 1/( tagged by: Max@Math Revolution This topic has 3 expert replies and 1 member reply GMAT/MBA Expert If 1/n(n+1) = 1/n - 1/(n+1), then what is the value of 1/( Timer 00:00 Your Answer A B C D E Global Stats Difficult [Math Revolution GMAT math practice question] If 1/n(n+1) = 1/n - 1/(n+1), then what is the value of 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100) A. 1/100 B. 1/50 C. 49/50 D. 99/100 E. 1/2 _________________ Math Revolution 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
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Newbie | Next Rank: 10 Posts Joined
17 Aug 2018
Posted:
9 messages
Hi,

Given function, 1/n*(n+1) = 1/n - 1/(n+1),

For patterns and sequences questions all we need to do is find initial few values and we will get to understand the pattern to solve the question.

1/(1*2) = 1/1 - ½

1/(2*3) = ½ - 1/3

1/(3*4) = 1/3 - ¼

We can clearly see that, adding the first three terms in the given sum, we will get 1 - ¼ = ¾

Similarly when we add the entire series,

1/1 -1/2 + ½ - 1/3 +……-1/99 + 1/99 -1/00

We will get only first term minus the term left, as all the other terms will get cancelled(subtracted) off

So,

1/1 - 1/100 = 99/100

Hope this helps.

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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

If 1/n(n+1) = 1/n - 1/(n+1), then what is the value of 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100)

A. 1/100
B. 1/50
C. 49/50
D. 99/100
E. 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

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=>
1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100)
= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + … + (1/99 - 1/100) = 1/1 - 1/100 = 1 - 1/100 = 99/100 after cancellation of the inner terms.

_________________ Math Revolution
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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 Email to : info@mathrevolution.com GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2801 messages Followed by: 18 members Upvotes: 43 Max@Math Revolution wrote: [Math Revolution GMAT math practice question] If 1/n(n+1) = 1/n - 1/(n+1), then what is the value of 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100) A. 1/100 B. 1/50 C. 49/50 D. 99/100 E. 1/2 Using the given formula, we have: 1/(1*2) = 1/1 - 1/2 1/(2*3) = 1/2 - 1/3 1/(3*4) = 1/3 - 1/4 1/(99*100) = 1/99 - 1/100 We see that the required sum is the sum of all the terms of the left hand side of the equal expressions above. Of course, that will be the sum of all the terms of the right hand side also. However, if we add up the terms on the right hand side, we see that we will have the first term of the first equal expressions, 1/1, and the last term of the last equal expressions, -1/100, left (since all the other terms cancel). Therefore, the sum is 1/1 - 1/100 = 99/100. Answer: D • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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