ziyuenlau wrote:Which of the following is the greatest?
(A) (1/√2)+(1/√4)+(1/√6)+(1/√8)
(B) [1/(2^2)]+[1/(4^2)]+[1/(6^2)]+[1/(8^2)]
(C) [1/(2^2)]+[1/(2^4)]+[1/(2^6)]+[1/(2^8)]
(D) 1-(1/2)+(1/4)-(1/6)
(E) (1/2)+(1/4)+(1/6)+(1/8)
Source : GMATNinja
OA=A
For a number greater than 1, say 'a,'
1/√a > 1/a > 1/a^2;
For example, say a = 2, then 1/2 = 0.5; 1/√2 = 1/1.414 = 0.707; 1/2^2 = 1/4 = 0.25
With these results in mind, let's analyze the values of the options.
(A) (1/√2)+(1/√4)+(1/√6)+(1/√8): It can be greatest as the four terms are of form 1/√a.
(B) [1/(2^2)]+[1/(4^2)]+[1/(6^2)]+[1/(8^2)]: Compared with Option A, it cannot be the greatest as the four terms are of form 1/a^2.
(C) [1/(2^2)]+[1/(2^4)]+[1/(2^6)]+[1/(2^8)]: Compared with Option B, it cannot be the greatest as its last two terms are less than the respective last two terms of Option B.
(D) 1-(1/2)+(1/4)-(1/6) = 1/2 + 1/12: Compared with Option A, it cannot be the greatest as its last term (1/12) is less than each of the last three terms of Option A.
(E) (1/2)+(1/4)+(1/6)+(1/8): compared with Option A, it cannot be the greatest as the four terms are of form 1/a.
The correct answer:
A
Hope this helps!
Relevant book:
Manhattan Review GMAT Math Essentials Guide
-Jay
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