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(1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following

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(1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following  [#permalink]

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New post Updated on: 18 Aug 2017, 22:45
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Question Stats:

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(1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following ranges?


A. (1/6)~(1/5)
B. (1/5)~(1/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1

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Originally posted by MathRevolution on 24 Jan 2016, 15:48.
Last edited by abhimahna on 18 Aug 2017, 22:45, edited 2 times in total.
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Re: (1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following  [#permalink]

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New post 24 Jan 2016, 15:57
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3
MathRevolution wrote:
(1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following ranges?


A. (1/6)~(1/5)
B. (1/5)~91/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1


* A solution will be posted in two days.


The given sequence will have a sum between 32/64 and 32/33 as shown below.

Number of terms in the given series = 32.

The lowest term is 1/64 , the largest being 1/33.

Thus, the sum of the given series will be more than

1/64 + 1/64.....1/64 (32 times)

---> 32*(1/64) = 32/64 = 1/2 and

less than 1/33 + 1/33...... 1/33 (32 times)

---> 32*(1/33) = 32/33 = 1 (approx)

E is thus the correct answer.
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Re: (1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following  [#permalink]

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New post 26 Jan 2016, 18:14
(1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following ranges?


A. (1/6)~(1/5)
B. (1/5)~91/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1


==> The sum of consecutive reciprocal numbers is determined by the first and the last terms. Also, the number of franctions is 64-33+1=32. Then, if S=(1/33)+(1/34)+……+(1/63)+(1/64), it becomes 32/64<S<32/33, and 1/2=32/64<S<32/33<1 -> 1/2<S<1. Therefore, the answer is E.
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Re: (1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following  [#permalink]

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Re: (1/33)+(1/34)+……+(1/63)+(1/64) is including in which of the following &nbs [#permalink] 27 Aug 2018, 22:50
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