if we follow all the way into algebra and find the formula for all n-s then we end up in something like 4(n!*n!/2 + n!*n!/3 + ... )/n!*n!
Instead I would use the shortcut and look into the first term which is 2 and the last term which is (4/100 - 4/101). It's clear that the answer cannot be 2 or 0 or even negative value as we have the positive value sequence and the first term is already 2. The only options are 3 and 4, so we narrowed the choices to "2 out of 5", better now ... and either D or E
To evaluate what is the answer I would propose, completing some more values here. We know by simple plugging into sequence function 4/(n^2+n) the 2nd term is 2/3 and the 3rd, 4th and 5th terms will be 1/3, 1/5, 2/15. Thus, (2/3 + 1/3 +1/5 +2/15) is (20+10+6+4)/30=4/3 OR greater than 1. We definitely cannot select answer D now as the resultant is more than 3, we have to mark choice E
correct answer e
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
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
algebra
Source: Beat The GMAT — Problem Solving |
-
neelgandham
- Community Manager
- Posts: 1060
- Location: Utrecht, The Netherlands
- Thanked: 318 times
an = (4/n)-(4/(n+1))
a1 = 4/1 - 4/2
a2 = 4/2 - 4/3
a3 = 4/3 - 4/4
.
.
.
.
a99 = 4/99 - 4/100
a100 = 4/100 - 4/101
a1 + a2 + ....a99 + a100 = 4/1 - 4/2 + 4/2 - 4/3 + 4/3 - 4/4.........+ 4/99 - 4/100 + 4/100 - 4/101
If you observe, except for the values at the extremes, i.e., 4/1 and -4/101, rest cancel out. So,
a1 + a2 + ....a99 + a100 = 4/1 - 4/101 = 4 - 4/100(approx) = ~ 3.96
Answer E
a1 = 4/1 - 4/2
a2 = 4/2 - 4/3
a3 = 4/3 - 4/4
.
.
.
.
a99 = 4/99 - 4/100
a100 = 4/100 - 4/101
a1 + a2 + ....a99 + a100 = 4/1 - 4/2 + 4/2 - 4/3 + 4/3 - 4/4.........+ 4/99 - 4/100 + 4/100 - 4/101
If you observe, except for the values at the extremes, i.e., 4/1 and -4/101, rest cancel out. So,
a1 + a2 + ....a99 + a100 = 4/1 - 4/101 = 4 - 4/100(approx) = ~ 3.96
Answer E
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
