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
Thanks.
Sum of Reciprocals
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- logitech
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1/91 + ...... + 1/100 = S We have 10 terms
If they were all 1/91 Then S = 10/91
If they were all 1/100 Then S = 10/100
So,
1/10 < S < 10/91
which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
I AM EDITING THIS PART:
S>1/10
So yes 1/10 is less than S - Duh!!
If they were all 1/91 Then S = 10/91
If they were all 1/100 Then S = 10/100
So,
1/10 < S < 10/91
which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
I AM EDITING THIS PART:
S>1/10
So yes 1/10 is less than S - Duh!!
Last edited by logitech on Thu Jan 01, 2009 11:28 pm, edited 1 time in total.
LGTCH
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1/10 is definitely less than S
i'm going with (C)
i'm going with (C)
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- ronniecoleman
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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 II
1/90 + 1/91 + 1/92 ........ > 1/100 * 10
since 1/90 > 1/100
1/91 > 1/100
1/90 + 1/91 .... < 1/90 * 10
since 1/91 < 1/90
1/92 < 1/90
So choose C
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 II
1/90 + 1/91 + 1/92 ........ > 1/100 * 10
since 1/90 > 1/100
1/91 > 1/100
1/90 + 1/91 .... < 1/90 * 10
since 1/91 < 1/90
1/92 < 1/90
So choose C
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Awesome approach Logitech!logitech wrote:1/91 + ...... + 1/100 = S We have 10 terms
If they were all 1/91 Then S = 10/91
If they were all 1/100 Then S = 10/100
So,
1/10 < S < 10/91
which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
I AM EDITING THIS PART:
S>1/10
So yes 1/10 is less than S - Duh!!