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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

sequence -1

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 227
Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members
Thanked: 12 times
by guerrero » Fri Apr 12, 2013 1:11 am
The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 100 terms of the sequence?

A. 201/100
B. 99/100
C. 100/101
D. 1/10000
E. 0

OA c
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members
Location: Delhi, India
Thanked: 344 times

by Anju@Gurome » Fri Apr 12, 2013 1:16 am
guerrero wrote:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 100 terms of the sequence?
1st term = 1/1 - 1/(1 + 1) = 1/1 - 1/2
2nd term = 1/2 - 1/(2 + 1) = 1/2 - 1/3
3rd term = 1/3 - 1/(3 + 1) = 1/3 - 1/4
4th term = 1/4 - 1/(4 + 1) = 1/4 - 1/5
...

we can see that if we keep adding each term, second part of each term will be cancelled by the first part of the next term. Eventually the sum will be equal to (first part of 1st term - second part of last term).

Hence, sum of first 100 terms = 1/1 - 1/(100 + 1) = 1 - 1/101 = 100/101

The correct answer is C.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1