for every integer k, from 1 to 10 inclusive, the kth term of a sequence is given by -1^(k+1) * (1/2^k) If T is the sum of the first ten digits, T is
between 1 and 2
between 1/2 and 1
between 1/4 and 1/2
less than 1/4
I know how to solve it the long way... but the GMAT doesn't want us to do that... so just wondering how others worked the problem
T = (1/2) - (1/4) + (1/8) - (1/16) + ... and so on.
The answer would be D.
There is no real need to solve this problem actually.
Lets look at the first 2 terms, 1/2 and 1/4. Their difference is 1/4. Then you add (1/8) and the difference is now between 1/2 and 1/4.
Now you subtract 1/16 and still the result is between 1/2 and 1/4.