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(b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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(b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90  [#permalink]

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25 Feb 2019, 01:10
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Difficulty:

45% (medium)

Question Stats:

61% (02:00) correct 39% (02:32) wrong based on 33 sessions

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(b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90?

A. 4/5
B. 5/6
C. 8/9
D. 9/10
E. 11/12

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Re: (b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90  [#permalink]

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25 Feb 2019, 02:15
MathRevolution wrote:
(b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90?

A. 4/5
B. 5/6
C. 8/9
D. 9/10
E. 11/12

(b-a)/ab = 1/a – 1/b

1/2 + 1/6 + 1/12 + … + 1/90 ==> (1-1/2)+(1/2-1/3)+ .........+(1/9-1/10)

==>1-1/10 ==> 9/10

Hence D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: (b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90  [#permalink]

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27 Feb 2019, 05:18
1/2 + 1/6 + 1/12 + … + 1/90
= 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1(9*10)
= (2-1)/(1*2) + (3-2)/(2*3) + (4-3)/(3*4) + … + (10-9)/(9*10)
= (1/1 – 1/2) + (1/2 – 1/3) + (1/3-1/4) + … + (1/9 – 1/10)
= 1/1 – 1/10
= 9/10

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Re: (b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90  [#permalink]

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02 Mar 2019, 09:17
MathRevolution wrote:
(b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90?

A. 4/5
B. 5/6
C. 8/9
D. 9/10
E. 11/12

1/2 = 1 - 1/2

1/6 = 1/2 - 1/3

1/12 = 1/3 - 1/4

1/90 = 1/9 - 1/10

Adding the above equations, we have:

1/2 + 1/6 + 1/12 + … + 1/90 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + … + 1/9 - 1/10

We see all the terms on the right hand side cancel except 1 and -1/10; therefore,

1/2 + 1/6 + 1/12 + … + 1/90 = 1 - 1/10

1/2 + 1/6 + 1/12 + … + 1/90 = 9/10

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Re: (b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90   [#permalink] 02 Mar 2019, 09:17
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