The answer is D

--------------------------------------------------------------------------------

Q. 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) > 2

b) between 1 and 2

c) between 1/2 and 1

d) between 1/4 and 1/2

e) less then 1/4

T1 = (-1)^2*(1/2)^1= 1/2

T2= (-1)^3*(1/2)^2 = -1/4

T3= (-1)^4*(1/2)^3 = + 1/8

.

.

T9= (-1)^10*(1/2)^9= (1/2)^9

t10=(-1)^11*(1/2)^10= - (1/2)^10

1/2 - 1/4 = 1/4 + 1/8 = 3/8 - 1/16 = 5/16 + 1/32 = 11 /32 - 1/64 = 21 / 64 + 1/128 = 43 / 128

since you are summing, the number is going to slowly move between 1/4 and 1/2 but staying above 1/4 and below 1/2. It keeps moving by smaller and smaller fractions, but it always will be above 1/4 and under 1/2. Look at it this way. The first two numbers establish the range. It starts at a 1/2 then drops to 1/4 and each time it lowers and raises by a smaller increment. What you will have is something that looks like this:

..

....

.......

........

...........

.............

.................

.............

...........

.........

.......

....

..

meaning, first the number swings a lot, then it slowly swings by increasingly an infinitely smaller increments. Eventually you are adding 1/10000000 and then subtracting 1/100000000 and so on into infinity.

Long story short, you have the number .5 and .25. The number made by this sum will just keep getting more and more decimal places instead of moving past one of those two numbers.

I really hope this long ass explanation is right or it will look pretty stupid

.

I'm sitting in Norway and its almost 1am, so who knows.