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

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SVP
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S is the sum of the reciprocal of a list of consecutive [#permalink] New post 09 Jun 2006, 09:42
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A
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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
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Re: PS sum of reciprocals [#permalink] New post 09 Jun 2006, 09:55
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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 [#permalink] New post 09 Jun 2006, 09:56
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
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Re: PS sum of reciprocals [#permalink] New post 09 Jun 2006, 10:05
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...
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 [#permalink] New post 10 Jun 2006, 18:58
how can you have a range of a number?

i thought ranges apply to sets?

pelase explain!
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 [#permalink] New post 10 Jun 2006, 19:06
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" :)
  [#permalink] 10 Jun 2006, 19:06
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