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Consecutive integers

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Consecutive integers

by alex.gellatly » Thu Jun 28, 2012 5:17 pm
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I. 1/8
II. 1/9
III 1/10

A. None
B. I only
C. III only
D. II and III only
E. I, II, and III

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by Anurag@Gurome » Thu Jun 28, 2012 5:55 pm
alex.gellatly wrote:If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
S = (1/91 + 1/92 + ... + 1/100)

Note that each of the terms in the expression of S are less than or equal to 1/100.
As there are 10 terms, S > 10*(1/100) = 1/10

By similar logic, S < 10*(1/90) = 1/9
Hence, S < 1/8

The correct answer is C.
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