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# If 1/n(n+1) = 1/n - 1/(n+1), then what is the value of 1/(

tagged by: Max@Math Revolution

00:00

A

B

C

D

E

## Global Stats

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[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
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Only $99 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 ### Top Member Newbie | Next Rank: 10 Posts Joined 17 Aug 2018 Posted: 4 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 So the answer is D. Hope this helps. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12123 messages Followed by: 1237 members Upvotes: 5254 GMAT Score: 770 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 _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Legendary Member Joined 24 Jul 2015 Posted: 1590 messages Followed by: 27 members Upvotes: 19 GMAT Score: => 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. Therefore, the answer is D. Answer: D _________________ 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$99 for 3 month Online Course
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### GMAT/MBA Expert

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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
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.

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