Sums and what not?

You are getting it wrong because there are alternating signs.

This is one way you could look at it. There are others.

T = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + ...
= (1/2 - 1/4) + (1/8 - 1/16) + (1/32 - 1/64) + ...
= 1/4 + 1/16 + 1/64 + ...

This sum will be a little bit more than a quarter. Thus answer D.

moutar wrote:You are getting it wrong because there are alternating signs.

This is one way you could look at it. There are others.

T = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + ...
= (1/2 - 1/4) + (1/8 - 1/16) + (1/32 - 1/64) + ...
= 1/4 + 1/16 + 1/64 + ...

This sum will be a little bit more than a quarter. Thus answer D.

this in fact forms a geometric progression whose first tem and common ratio is each 1/4, since the common ratio is between 0 and 1, hence the sum to an infinite number of such terms would still be finite and will be equal to (1/4)/[1 - (1/4)] = 1/3. Choose the most suitable interval.