Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 17 Jul 2019, 19:53

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

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

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
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, 02:01
1
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:53) correct 35% (02:29) wrong based on 130 sessions

HideShow timer Statistics


Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
G
Joined: 19 Apr 2016
Posts: 271
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, 02:20
5
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-)
General Discussion
Manager
Manager
avatar
S
Joined: 05 Apr 2014
Posts: 138
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, 02:27
1
1
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, 14:24
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))...
Intern
Intern
avatar
Joined: 07 May 2018
Posts: 3
GMAT 1: 660 Q39 V41
For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)  [#permalink]

Show Tags

New post 30 Nov 2018, 07:43
I didn't pick up on the pattern while calculating a1, a2, a3; however, I did a couple of sums and picked up on the pattern then:
a1=1/2
a1+a2=2/3
a1+a2+a3=3/4

so a1+a2+....+a100=100/100+1=100/101
LBS Moderator
User avatar
D
Joined: 04 Jun 2018
Posts: 587
Location: Germany
Concentration: General Management, Finance
GMAT 1: 730 Q47 V44
GPA: 3.4
WE: Analyst (Transportation)
Premium Member Reviews Badge
Re: For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)  [#permalink]

Show Tags

New post 26 Jun 2019, 08:51
Bunuel

Are you sure this is a Veritas Prep question?

I am fairly certain that this question is actually from the GMAT Prep EP2 or a pretty blatant copy of an OG question.

https://gmatclub.com/forum/for-every-po ... 17215.html

Best regards,
Chris
_________________
Intern
Intern
avatar
B
Joined: 30 May 2019
Posts: 4
GPA: 3
Reviews Badge
Re: For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)  [#permalink]

Show Tags

New post 26 Jun 2019, 09:12
100/101
--->

a1= 1/1- 1/2
a2 = 1/2 -1/3
a3 = 1/3 -1/4
a4 = 1/4 -1/5
.
.
.
a100=1/100-1/101

the second term of the previous term and the first term of the present term get cancelled out (e.g 1/2 from a1 and 1/2 from a3 get cancelled out)
... leaving only 1/1 and 100/101

Thus, 1/1-1/101 = 101/101-1/101 = 100/101
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6923
Location: United States (CA)
Re: For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)  [#permalink]

Show Tags

New post 01 Jul 2019, 17:14
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


Let’s calculate the first few terms:

a1 = 1/1 - 1/2

a2 = 1/2 - 1/3

a3 = 1/3 - 1/4

a4 = 1/4 - 1/5

Summing the first 4 terms of the sequence, we have 1 - 1/5 because all the middle numbers cancel. Thus, we see that only the first and last term are left. So the sum of the first 100 terms would be 1 - 1/101 = 100/101.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1)   [#permalink] 01 Jul 2019, 17:14
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  





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