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Of the following sums, which is greatest ?

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Of the following sums, which is greatest ? [#permalink] New post 24 Jun 2009, 02:39
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Of the following sums, which is greatest ?

(A) 1/root 2 + 1/root 3+ 1/root 4+ 1/root 5

(B) 1/2^2 + 1/3^2 + 1/4^2 + 1/5^2

(C) 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5

(D)1-1/2+1/3-1/4

(E) 1/2+1/3+1/4 +1/5

OA:A

Which is the easiest and fastest way to solve this problem??
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Re: Of the following sums, which is greatest ? [#permalink] New post 24 Jun 2009, 02:45
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This question is rather easy. Since the numerators are same. You will compare the denominators. The biggest denominator is the smallest number.
root n < n < n^2 < 2^n for almost every number (some are not but as n grows inequality holds true)
So B,C and E are smaller than A. Since E is greater than D. A is the biggest.
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Re: Of the following sums, which is greatest ? [#permalink] New post 24 Jun 2009, 03:02
maliyeci wrote:
This question is rather easy. Since the numerators are same. You will compare the denominators. The biggest denominator is the smallest number.
root n < n < n^2 < 2^n for almost every number (some are not but as n grows inequality holds true)
So B,C and E are smaller than A. Since E is greater than D. A is the biggest.


Kudos to you. I had a similar solution in my mind, except for an explanation for option D.
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Re: Of the following sums, which is greatest ?   [#permalink] 24 Jun 2009, 03:02
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