here the first term is (-1) ^ k+1

for k = 1;
when you start calculating it the first number will be -1^2 = 1
and the (1/2)^k i.e. 1/2
so first term will be 1*1/2= 1/2

when k = 2;
(-1) ^ k+1 will be -1
and (1/2) ^ k = 1/4
so the second term will be -1 * 1/4 = -1/4
the sequence will continue... the next number will be positive and the number after that will be negative.

1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 .... - 1/1024

lokking the this my guess was ans between 1/2 and 1/4; as the numbers ahead are getting more and more negligible.

you can select E. less than 1/4; but intelligent guess will be between 1/4 and 1/2;

if you go on and calculate the sequence; it gives 341/1024 = 0.33 i.e. approx 1/3

Ans D

makes sense...thanks.

A slightly simpler way of looking at it.

The terms will alternate between positive and negative. Pair up each positive and negative term, and look at the pattern.

(1/2 – 1/4) + (1/8 – 1/16) + …
=1/4 + 1/16

1/4 is large, and every term being added after that is decreasingly smaller. Thus the sum will be greater than 1/4, but not by much. Which leaves (D).

given seq = -1^k + (1/2)^k...now the term -1^k will be -1 for K with odd value and +1 for K with even value...in the 1st 10 numbers we'll have alternate -1 and +1 which will sum to ZERO...guys this is the main catch..we're then left with sum of (1/2)^k...now as the seq goes to infinity the value nears (1/2)/(1-1/2) = 1..so for 1st ten terms the sum shld be b/w 1/2 and 1...which is C.