It is currently 24 Feb 2018, 06:08

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43894
For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1) [#permalink]

Show Tags

New post 20 Feb 2017, 01:01
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:38) correct 36% (02:01) wrong based on 75 sessions

HideShow timer Statistics

For the sequence a1, a2, a3 ... an, an is defined by \(a_n=\frac{1}{n}−\frac{1}{(n+1)}\) for each integer n≥1. What is the sum of the first 100 terms of this sequence?

A. 100/99

B. 101/100

C. 100/101

D. 99/100

E. 999/1010
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Senior Manager
Senior Manager
User avatar
G
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1) [#permalink]

Show Tags

New post 20 Feb 2017, 01:20
2
This post received
KUDOS
Bunuel wrote:
For the sequence a1, a2, a3 ... an, an is defined by \(a_n=\frac{1}{n}−\frac{1}{(n+1)}\) for each integer n≥1. What is the sum of the first 100 terms of this sequence?

A. 100/99

B. 101/100

C. 100/101

D. 99/100

E. 999/1010


\(a_n=\frac{1}{n}−\frac{1}{(n+1)}\)

\(a_1 + a_2 + a_3 + a_4 + ......+ a_99 + a_100=\frac{1}{1}−\frac{1}{2}+\frac{1}{2}−\frac{1}{3}+\frac{1}{3}−\frac{1}{4}+\frac{1}{4}−\frac{1}{5}+.....+ \frac{1}{99}−\frac{1}{100}+\frac{1}{100}−\frac{1}{101}\)

Everything in between 1/1 and -(1/101) gets cancelled out.

\(a_1 + a_2 + a_3 + a_4 + ......+ a_99 + a_100= \frac{1}{1}−\frac{1}{101} = \frac{100}{101}\)

Hence Option C is correct.
Hit Kudos if you liked it 8-)
1 KUDOS received
Manager
Manager
avatar
S
Joined: 05 Apr 2014
Posts: 147
Location: India
Concentration: Economics, International Business
Schools: ISB '19, Fox"19
GMAT 1: 660 Q48 V33
GPA: 3
Re: For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1) [#permalink]

Show Tags

New post 20 Feb 2017, 01:27
1
This post received
KUDOS
C
Coz
a1= 1- 1/2
a2 = 1/2 -1/3

a100= 1/100 - 1/101
Adding all d above we get

1-1/101 = 100/101

Sent from my HM 1S using GMAT Club Forum mobile app
Intern
Intern
avatar
Joined: 21 Jan 2018
Posts: 1
Re: For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1) [#permalink]

Show Tags

New post 21 Jan 2018, 13:24
Just curious why the each term would not be included in parenthesis? Wouldn't this change the order of operations and the answer?

(A1)+(a2)...
1/2+((1/2)-(1/3))+((1/3)-(1/4))...
Re: For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)   [#permalink] 21 Jan 2018, 13:24
Display posts from previous: Sort by

For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.