Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

For the sequence \(a_1, a_2, a_3 \cdots a_n,\) \(a_n\) is defined by \(a_n=\dfrac1{n}-\dfrac1{n+1}\) for each integer

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Moderator
Posts: 2058
Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members
Thanked: 1 times
by M7MBA » Fri Aug 06, 2021 10:35 am
Timer
00:00
Your answer
Difficulty–

right wrong

Pick an answer to see how members did

For the sequence \(a_1, a_2, a_3 \cdots a_n,\) \(a_n\) is defined by \(a_n=\dfrac1{n}-\dfrac1{n+1}\) for each integer \(n\ge 1.\) What is the sum of the first \(100\) terms of this sequence?

A. \(\dfrac{100}{99}\)

B. \(\dfrac{101}{100}\)

C. \(\dfrac{100}{101}\)

D. \(\dfrac{99}{100}\)

E. \(\dfrac{999}{1010}\)

Answer: C

Source: Veritas Prep
Top
Join the discussion
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16206
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Re: For the sequence \(a_1, a_2, a_3 \cdots a_n,\) \(a_n\) is defined by \(a_n=\dfrac1{n}-\dfrac1{n+1}\) for each intege

by Brent@GMATPrepNow » Sun Aug 08, 2021 5:54 am
M7MBA wrote: ↑
Fri Aug 06, 2021 10:35 am
 For the sequence \(a_1, a_2, a_3 \cdots a_n,\) \(a_n\) is defined by \(a_n=\dfrac1{n}-\dfrac1{n+1}\) for each integer \(n\ge 1.\) What is the sum of the first \(100\) terms of this sequence?

A. \(\dfrac{100}{99}\)

B. \(\dfrac{101}{100}\)

C. \(\dfrac{100}{101}\)

D. \(\dfrac{99}{100}\)

E. \(\dfrac{999}{1010}\)

Answer: C

Source: Veritas Prep
term1 = 1/1 - 1/2
term2 = 1/2 - 1/3
term3 = 1/3 - 1/4
term4 = 1/4 - 1/5
.
.
.
term99 = 1/99 - 1/100
term100 = 1/100 - 1/101

So, the sum looks like this:

Sum = (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .... + (1/99 - 1/100) + (1/100 - 1/101)

NOTICE THAT MOST TERMS CANCEL OUT

Sum = (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .... + (1/99 - 1/100) + (1/100 - 1/101)
= 1/1 - 1/101
= 101/101 - 1/101
= 100/101

Answer: C
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion