ddm wrote:help

kth term =(-1)^(k+1) * 1/2^k

1st term = (-1)^2 * 1/2^1 = 1/2
2nd term = -1/4
3rd term = 1/8
4th term = -1/6
so on and so forth

T = 1/2 - 1/4 + 1/8 - 1/16+......1/1024

1/2-1/4 = 1/4
1/8-1/16 = 1/8
so on and so forth

T = 1/4+1/16+1/64+....+1/1024

the sum will be between 1/4 and 1/2

Hence D is the answer.

There is pattern we can see in this problem similar to parallel+chase said but I will try to explain this a little.

Knowing the powers of 2 till 512 will come in handy in this situation

1/2-1/4+1/8-1/16+1/32-1/64+1/128-1/256+1/512

If we take the lcm 512 you will see a pteern on the numerator terms.

It will be 256(which is 2^8)-128(which is 2^7)+64 (which is 2^6) -32 (which is 2^5 so on...)+16-8+4-2+1

i.e 256-128+64 -32+16-8+4-2+1/512 = .3

The answer is D) between 1/4 and 1/2

There is pattern we can see in this problem similar to what parallelchase said but I will try to explain this a little.

Knowing the powers of 2 till 512 will come in handy in this situation

1/2-1/4+1/8-1/16+1/32-1/64+1/128-1/256+1/512

If we take the lcm 512 you will see a pattern develop on the numerator terms.

It will be 256(which is 2^-128(which is 2^7)+64 (which is 2^6) -32 (which is 2^5 so on...)+16-8+4-2+1

i.e 256-128+64 -32+16-8+4-2+1/512 = .3

The answer is D) between 1/4 and 1/2