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What is the scope including 1/11+1/12+1/13+......+1/20?

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What is the scope including 1/11+1/12+1/13+......+1/20? [#permalink]

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New post 24 Jul 2016, 02:09
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E

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74% (00:48) correct 26% (01:37) wrong based on 61 sessions

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What is the scope including 1/11+1/12+1/13+......+1/20?
A 1/6~1/5
B. 1/5~1/4
C. 1/4~1/3
D. 1/3~1/2
E. 1/2~1

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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Re: What is the scope including 1/11+1/12+1/13+......+1/20? [#permalink]

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New post 24 Jul 2016, 04:29
MathRevolution wrote:
What is the scope including 1/11+1/12+1/13+......+1/20?
A 1/6~1/5
B. 1/5~1/4
C. 1/4~1/3
D. 1/3~1/2
E. 1/2~1

*An answer will be posted in 2 days.


For Maximum value : It should be less than 1/11 + 1/11 +1/11... 10 times = 10/11 ~ 1

For Minimum Value : It should be greater than 1/20+ 1/2-+ 1/20 .. 10 times = 10/20 = 1/2.

Thus, the answer should lie between 1/2 and 1. Correct ans : E.
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Re: What is the scope including 1/11+1/12+1/13+......+1/20? [#permalink]

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New post 25 Jul 2016, 10:38
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If you want a more precise answer:

You know there are 10 numbers and first value is \(\frac{1}{11}\) and last value is \(\frac{1}{20}\)

So

\(Avg = \frac{First + Last}{2} = \frac{31}{440}\)

Then

\(Sum = Avg * n = \frac{31}{440}*10 =\frac{31}{44} \approx{\frac{3}{4}}\)

Answer E.

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Re: What is the scope including 1/11+1/12+1/13+......+1/20? [#permalink]

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New post 25 Jul 2016, 18:32
The sum of a sequence of reciprocals is determined by the first and the end term. So, since 1/2=10/20<1/11+1/12+1/13+......+1/20<10/11<10/10=1, the correct answer is E.
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Re: What is the scope including 1/11+1/12+1/13+......+1/20? [#permalink]

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New post 07 Oct 2017, 02:00
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Re: What is the scope including 1/11+1/12+1/13+......+1/20?   [#permalink] 07 Oct 2017, 02:00
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