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20 Mar 2011, 03:46
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (02:14) correct
50%
(02:18)
wrong
based on 18
sessions
History
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Time
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Not Attempted Yet
For every integer k from 1 to 10, kth term of a certain sequence can be written as [(-1)^(k+1)]*(1/2^k). If T is the sum of first 10 terms in the sequence, then T is
a) greater than 2
b) between 1 and 2
c) between 1/2 and 1
d) between 1/4 and 1/2
e) less than 1/4
OA is provided.
I want to know how to solve for this.
a) greater than 2
b) between 1 and 2
c) between 1/2 and 1
d) between 1/4 and 1/2
e) less than 1/4
OA is provided.
I want to know how to solve for this.
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bagrettin
Joined: 03 Mar 2011
Last visit: 01 Mar 2012
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Location: United States
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GPA: 3.9
20 Mar 2011, 04:03
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If we will write this sum, this will be
0.5-0.5^2+0.5^3-...-0.5^10=0.5(1-0.5)+0.5^2(1-0.5)+...+0.5^5(1-0.5)=(1-0.5)(0.5+0.5^2+...+0.5^5)= 0.5^2+0.5^3+0.5^4+0.5^5+0.5^6
Then you could use the formula for a sum of a geometric progression or just calculate directly. It is
1/4+1/8+1/16+1/32+1/64=(16+8+4+2+1)/64=31/64
Hence the answer is D
0.5-0.5^2+0.5^3-...-0.5^10=0.5(1-0.5)+0.5^2(1-0.5)+...+0.5^5(1-0.5)=(1-0.5)(0.5+0.5^2+...+0.5^5)= 0.5^2+0.5^3+0.5^4+0.5^5+0.5^6
Then you could use the formula for a sum of a geometric progression or just calculate directly. It is
1/4+1/8+1/16+1/32+1/64=(16+8+4+2+1)/64=31/64
Hence the answer is D
