GMAT Question 14

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 1st 10 terms in the sequence then T is,  a)Greater than 2 
b)between 1 and 2 
c)between ½ and 1 
d)between ¼ and ½ 
e)less than ¼

Solution:
Kth term of a sequence is =  Rk = (-1)^k+1 * (1/2^k)  
R1 = (-1)^2 * (1/2)^1 = 1/2 
R2 = (-1)^3 * (1/2)^2 = -1/4  similarly,
R3= 1/8, R4 = -1/16 etc  
So sum of 1st 10 terms in the sequence =  S = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 +1/128 etc up to the 10th term ( there will be total of 11 terms as S is inclusive of 1st and 10 term)  

S = 1/2 +(- 1/4 + 1/8) + (- 1/16 + 1/32) etc ( there will be a total of 5 pairs like this as the sequence has 11 terms. ) 
S = 1/2 -1/8 -1/32 etc  

If we sum up the negative terms 
1/8 + 1/32 +.... we can see that sum is greater than 1/8 but less than 1/4 ( as 1/32+1/128 etc <1/8) 
 So the sum is greater than 1/2-1/4 =1/4 but less than 1/2 as we are subtracting 1/8 + 1/32 from 1/2  Hence the sum is between 1/2 and 1/4

 Answer is D