Problem Solving

Hi, I've seen this somewhere but can't locate the explanation - could someone help me? (I understand the pattern is 1/2, -1/4, 1/8, -1/16....but not sure how it's connected to get answer )


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..

1 greater than 2
2 between 1 and 2
3 betwee 1/2 and 1
4 between 1/4 and 1/2
5 less than 1/4

I just happened to solve this.. This question is from GMAT PREP

This is how I did

The series you have mentioned is correct and is GP

T = [1/2(1-(-1/2)^10]/(1-(-1/2))

Solving this gives 1/3 - (1/3)*(1/2^10)

Since the sum is less than 1/3 answers 1, 2 and 3 are eliminated

Now, the second term in above equation is smaller that 1/12 (difference of 1/3 and 1/4) so total will NOT be less than 1/4

So, ANS 4

kajcha, Thanks - I have to remember GP formula...