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Sum of Reciprocals

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Senior | Next Rank: 100 Posts
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by duke » Thu Jan 01, 2009 8:29 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

Thanks.
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Re: Sum of Reciprocals

by logitech » Thu Jan 01, 2009 8:42 pm
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!!
Last edited by logitech on Thu Jan 01, 2009 11:28 pm, edited 1 time in total.
LGTCH
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by Bidisha800 » Thu Jan 01, 2009 10:43 pm
1/10 is definitely less than S

i'm going with (C)
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by ronniecoleman » Fri Jan 02, 2009 12:38 am
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
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by rahul.s » Fri Jan 22, 2010 3:09 am
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!!
Awesome approach Logitech! :D
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