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M is the sum of the reciprocals of the consecutive integers

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M is the sum of the reciprocals of the consecutive integers [#permalink] New post 07 Jun 2012, 00:14
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78% (01:55) correct 22% (01:27) wrong based on 67 sessions
M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?

A. 1/3 < M < 1/2
B. 1/5 < M < 1/3
C. 1/7 < M < 1/5
D. 1/9 < M < 1/7
E. 1/12 < M < 1/9

OPEN DISCUSSION OF THIS QUESTION IS HERE: m-is-the-sum-of-the-reciprocals-of-the-consecutive-integers-143703.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Jul 2013, 06:01, edited 2 times in total.
Edited the question and added the OA
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Re: maths problem [#permalink] New post 07 Jun 2012, 01:39
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M = 1/201 + 1/202 + 1/203 + ...... + 1/300

If we replace the first 99 terms by 1/300, then we get a sum = 100/300 = 1/3. Since the actual terms are larger than 1/300, the sum is larger than 1/3.

If we replace the all the 100 terms by 1/200, we get a sum = 100/200 = 1/2. Since the actual terms are smaller than 1/200, the sum is less than 1/2.

Therefore 1/3 < M < 1/2

Choice A
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Re: M is the sum of the reciprocals of the consecutive integers [#permalink] New post 09 Jul 2012, 03:26
Is this is only way to do this?
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Re: M is the sum of the reciprocals of the consecutive integers   [#permalink] 09 Jul 2012, 03:26
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