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Here goes my answer
The term 1 will be 1/2
term 2 will be -1/4

similarly 1/8 , -1/16 and so on

term1 + term2
= 1/2 -1/4 = 1/4

similarly next sum will be 1/8 - 1/16
= 1/8

and the series will go on

so your sum will lie between 1/4 and 1/2
Ans IMO D

Thanks for the explanation and also suggestion of pasting small images(I didn't check size of the image before posting. Thanks for mentioning). It is correct OA D.

poonam1279 wrote:Thanks for the explanation and also suggestion of pasting small images(I didn't check size of the image before posting. Thanks for mentioning). It is correct OA D.

You are welcome

Actually I am on slow connection so it took lot of time downloading the image

The series is:

(1/2 - 1/4) + (1/8 - 1/16) + (1/32 - 1/64) + (1/128 -1/256) + (1/512 - 1/1024)

As you can see from the pairs, the first pair is by far the most important pair.

The rest of the pairs are yielding smaller numbers.

(1/2 - 1/4) = 1/4

So the sum will be greater than 1/4. T>1/4

The sum of the second pair: 1/16
The sum of the third pair is : 1/64
The sum of the fourth pair is: 1/256
The sum of the fifth pair is :1/1024

As you can the even if the 3rd,4th and 5th sum was : 1/6

The rest of the pair would total to : 4 x 1/16 = 1/4

So the rest of the pairs will sum up < 1/4.

1/4 < TOTAL SUM < 1/4+1/4

1/4 < Total Sum < 1/2