Gmat practice test question

TT wrote:This appeared on my practice test 1. Is there a short cut to do this without actually writing out the terms and adding them?

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:
greater than 2
between 1 and 2
between 1/2 and 1
between 1/4 and 1/2
less than 1/4

i don't think there's any short cut..

but i don't think it'll be that difficult to actually solve it out..(not too long)

first, you just need to realize that (-1)^(k+1) only changes the sign.

(1/2)^k will have 1024(2^10 or 32*32) as a denominator when you add all of them.

(512-256+128-64+32-16+8-4+2-1)/1024 = 341/1024 --> between 1/4 & 1/2...

is the answer right? didn't really take me that long to do it... sorry if i didn't really answer your question..

That's the right answer. Thanks!