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If K is the sum of reciprocals of the consecutive integers

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Senior Manager
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Joined: 25 Mar 2013
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Re: If K is the sum of reciprocals of the consecutive integers [#permalink]

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New post 13 Nov 2016, 15:04
Number's between 43 to 38 inclusive = 6 no's
Middle number [43+48][/2] = 45.5

1/45 x 6 = > 1/7 (Approximately)

C
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I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

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Re: If K is the sum of reciprocals of the consecutive integers [#permalink]

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New post 08 Feb 2017, 10:00
not sure if this is right but let me know if this method is correct

6(1/45 +1/46)/2 = 271/2170 = 1/8< k <1/7

271*8 = 2268
271*7 = 1897

so 2268 is close to 2170 than 1897 hence (C)

Bunuel pls let me know.

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Re: If K is the sum of reciprocals of the consecutive integers [#permalink]

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New post 25 Nov 2017, 15:18
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fozzzy wrote:
If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?

A. 1/12
B. 1/10
C. 1/8
D. 1/6
E. 1/4


We want the approximate sum of 1/43 + 1/44 + 1/45 + . . . + 1/48

Let's make the following observations about the upper and lower values:

Upper values: If all 6 fractions were 1/43, the sum would be (6)(1/43) = 6/43 ~ 6/42 = 1/7

Lower values: If all 6 fractions were 1/48, the sum would be (6)(1/48) = 6/48 = 1/8

From this we can conclude that 1/8 < K < 1/7

If K is between 1/8 and 1/7, then K must be closer to 1/8 than it is to 1/6

Answer = C

Cheers,
Brent
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Kudos [?]: 2747 [1], given: 364

Re: If K is the sum of reciprocals of the consecutive integers   [#permalink] 25 Nov 2017, 15:18

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If K is the sum of reciprocals of the consecutive integers

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