For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1)^(k+1) * (1/2^k). If T is the sum of the 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 1/2

Following is what I did to solve this problem:

Need to sum of first 10 terms in the sequence.
I know that odd terms in the sequence are : 1/2, 1/8, 1/32, 1/128, 1/512
I know that even terms in the sequence are: -1/4, -1/16, -1/64, -1/256, -1/1024
Subtracting each of the even terms from odd: I get: 1/4 + 1/8 + 1/32 + 1/256 + 1/1024
Adding them I get 341/1024. I realize it is slightly greather than 1/4 and less than 1/2. Hence D.

Is there a faster method to answer this question?