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# The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1)

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Intern
Joined: 04 Sep 2009
Posts: 41

Kudos [?]: 84 [0], given: 9

The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1) [#permalink]

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22 Sep 2012, 09:19
4
This post was
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Difficulty:

55% (hard)

Question Stats:

58% (01:32) correct 42% (01:57) wrong based on 155 sessions

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The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 100 terms of the sequence?

A. 201/100
B. 99/100
C. 100/101
D. 1/10000
E. 0
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Sep 2012, 09:31, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 84 [0], given: 9

Intern
Joined: 02 Nov 2009
Posts: 41

Kudos [?]: 65 [0], given: 8

Location: India
Concentration: General Management, Technology
GMAT Date: 04-21-2013
GPA: 4
WE: Information Technology (Internet and New Media)
Re: The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1) [#permalink]

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22 Sep 2012, 10:18
Given Xn = 1/n - (1/(n+1))
--> X1=1-(1/2)
X2=(1/2)-(1/3)
X3=(1/3)-(1/4)

x1+x2+x3 = 1-(1/4) as other terms gets cancelled out...

following the same approach x1+x2...+x100 =1-(1/101) =100/101
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KPV

Kudos [?]: 65 [0], given: 8

Manager
Joined: 18 Oct 2013
Posts: 83

Kudos [?]: 59 [0], given: 36

Location: India
Concentration: Technology, Finance
GMAT 1: 580 Q48 V21
GMAT 2: 530 Q49 V13
GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)
Re: The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1) [#permalink]

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20 Nov 2013, 10:50

X1=1-1/2
x2=1/2-1/3
x3=1/3-1/4
.....
x99=1/99-1/100
x100=1/100-1/101

sum=X1+X2+X3+....X100=1-1/2+1/2-1/3+.......1/99-1/100+1/100-1/101=1-1/101=100/101

.
.

Kudos [?]: 59 [0], given: 36

Non-Human User
Joined: 09 Sep 2013
Posts: 14843

Kudos [?]: 287 [0], given: 0

Re: The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1) [#permalink]

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24 Jun 2017, 07:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Kudos [?]: 287 [0], given: 0

Re: The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1)   [#permalink] 24 Jun 2017, 07:18
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