dvp wrote:This is question number 2 from
https://www.beatthegmat.com/198-level-70 ... 43783.html.....
Ques . (-1)^(k+1) . (1/2 ^ k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼
Answer : [spoiler]d (as per document)[/spoiler]
I was able to deduce the equ till ----> (-1 ) . (-1/2)^k.
how to proceed further?
We don't need to determine the exact sum. Compute only as much as is necessary to see the pattern.
Sum of the first two terms is 1/2 + ( -1/4) = 1/4.
Next term is 1/8.
Next term is -1/16.
Now we can see the pattern.
The sum increases by a fraction and then decreases by a fraction 1/2 the size. In other words, the sum will alternate between going up a little and then down a little less than it went up.
Since the sum of the first 2 terms is 1/4, and all of the fractions after the first two terms will be less than 1/4, the sum will end up somewhere between 1/4 and 1/2.
The correct answer is D.
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