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

Redeem

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.

★★★★★5.0559 reviews
Vote for Target Test Prep, Newsweek Readers’ Choice Awards 2026
NEWSWEEK READERS’ CHOICE 2026

BIG NEWS! Target Test Prep has been nominated, and they’d love your vote!

TTP has worked incredibly hard to build the best test prep experience possible, and winning Newsweek’s 2026 Readers’ Choice Award for Best Test Prep would mean a lot to them. If TTP has helped you, they’d be incredibly grateful for your vote. You can vote once each day through September 9.

Vote for TTP
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
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
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start 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 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Sum of Integers (really annoying)

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Wed Jun 01, 2016 6:23 am
WRITE IT OUT and LOOK FOR A PATTERN.

First term = 1/1 - 1/2 = 1/2.
Second term = 1/2 - 1/3 = 1/6.
Third term = 1/3 - 1/4 = 1/12.
Fourth term = 1/4 - 1/5 = 1/20.

Sum of the first 2 terms:
1/2 + 1/6 = 2/3.

Sum of the first 3 terms:
2/3 + 1/12 = 3/4.

Sum of the first 4 terms:
3/4 + 1/20 = 4/5.

In each case:
The NUMERATOR of the sum = the NUMBER OF TERMS.
THE DENOMINATOR of the sum = NUMERATOR + 1.

Thus:
Sum of the first 100 terms = 100/101.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Tue Apr 05, 2016 3:31 amFollowed by: 1 member

by AndreiGMAT » Wed Jun 01, 2016 7:00 am
Mitch, that is surely an interesting approach. Thank you.
But why "traditional" method doesn't work for me here?

My way of thinking:

a1 = 1/2
a100 = 1/10100
Number of integers = 100
Average = 5051/20200
Sum = (5051/20200)*100 = 5051/202

This method always worked with integers for me before.
What am I missing here?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Wed Jun 01, 2016 7:05 am
AndreiGMAT wrote:Mitch, that is surely an interesting approach. Thank you.
But why "traditional" method doesn't work for me here?

My way of thinking:

a1 = 1/2
a100 = 1/10100
Number of integers = 100
Average = 5051/20200
Sum = (5051/20200)*100 = 5051/202

This method always worked with integers for me before.
What am I missing here?
The method above is valid for an EVENLY SPACED SET: a set in which the difference between successive terms is always THE SAME.
Here, the first four terms -- 1/2, 1/6, 1/12, 1/20 -- indicate that the set is NOT evenly spaced.
The difference between 1/2 and 1/6 is not the same as the difference between 1/6 and 1/12.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 01, 2016 7:15 am
term(n) = 1/x - 1/(x+1)

What is the sum of the first 100 terms of this sequence?

A) 0
B) 1/101
C) 99/100
D) 100/101
E) 1
Another approach:
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
= [spoiler]100/101[/spoiler]
= D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Wed Jun 01, 2016 7:16 am
Alternate approach:

a� + a₂ + a₃ = (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4)
Notice that the portion in red CANCELS OUT, leaving only the FIRST FRACTION AND THE LAST FRACTION.
Thus:
a� + ... + a�₀₀ = (1/1 - 1/2)...+ (1/100 - 1/101).
Since the portion in red will cancel out, we get:
a� + ... + a�₀₀ = 1/1 - 1/101 = 100/101.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Tue Apr 05, 2016 3:31 amFollowed by: 1 member

by AndreiGMAT » Wed Jun 01, 2016 7:34 am
Thank you, this is new and extremely useful.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Wed Jun 01, 2016 9:05 am
Hi AndreiGMAT,

While this question looks complex, there's a great pattern-matching shortcut built into it - to recognize the pattern, you'll likely have to do a bit of work on the pad though.

We're asked for the sum of the first 100 terms in the given sequence, but the GMAT doesn't really expect you to add up all of that work by hand. I'm going to write down the first few terms as a reference, but I'm NOT going to do any of the math yet....

N=1 --> 1/1 - 1/2
N=2 --> 1/2 - 1/3
N=3 --> 1/3 - 1/4
N=4 --> 1/4 - 1/5
Etc.

Notice that when we subtract a fraction, we end up adding it right back in the next calculation (re: -1/2....+1/2....-1/3....+1/3), so a lot of that math 'cancels out.' The only terms that WON'T cancel out are 1/1 and the very last term.... -1/101

Thus, the sum of those first 100 terms ends up totaling 1/1 - 1/101 = 100/101

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1