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# S is the sum of the reciprocal of a list of consecutive

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SVP
Joined: 24 Sep 2005
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S is the sum of the reciprocal of a list of consecutive [#permalink]

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09 Jun 2006, 10:42
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S is the sum of the reciprocal of a list of consecutive integers from 201 to 300, inclusive. What is the range of S?

A. 2/3 to 1
B. 0 to 1
C. 1/3 to 1/2
D. 4/5 to 1
D. 1/101 to 1/100
VP
Joined: 21 Sep 2003
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Location: USA
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Re: PS sum of reciprocals [#permalink]

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09 Jun 2006, 10:55
laxieqv wrote:
S is the sum of the reciprocal of a list of consecutive integers from 201 to 300, inclusive. What is the range of S?

A. 2/3 to 1
B. 0 to 1
C. 1/3 to 1/2
D. 4/5 to 1
D. 1/101 to 1/100

S = 1/201+1/202+1/203+........+1/300
Each of the term 1/201, 1/202..... is < 1/200
S < 100*1/200 (100 terms, each less than 1/200)
S < 1/2

Similarly each of the term 1/201, 1/202 .... is > 1/300
S > 100*1/300
S > 1/3

Hence 1/3 < S < 1/2
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Director
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09 Jun 2006, 10:56
Hallo laxie,
IMO biiggest possible sum is 1/200*100=1/2
least possible sum is 1/300*100=1/3
then S belongs in C
VP
Joined: 29 Dec 2005
Posts: 1348
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Re: PS sum of reciprocals [#permalink]

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09 Jun 2006, 11:05
laxieqv wrote:
S is the sum of the reciprocal of a list of consecutive integers from 201 to 300, inclusive. What is the range of S?

A. 2/3 to 1
B. 0 to 1
C. 1/3 to 1/2
D. 4/5 to 1
D. 1/101 to 1/100

range = (300-200)/300 to (300-200)/201
range = 1/3 to 1/2 aapprox...
Director
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10 Jun 2006, 19:58
how can you have a range of a number?

i thought ranges apply to sets?

pelase explain!
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Posts: 1890
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10 Jun 2006, 20:06
willget800 wrote:
how can you have a range of a number?

i thought ranges apply to sets?

pelase explain!

The question is translated from those who just took the test. The use of "range" may not be precise but still does it convey a meaning of a "scope" or " the difference between the upper and lower limit of S"
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