For every integer k, from 1 to 10 inclusive, the kth term of the sequence is given by (-1)^k+1 (1/(2^k)).
What is the sum of the 10 terms?
1) greater than 2
2) between 1 and 2
3) between 1/2 and 1
4) between 1/4 and 1/2
5) less than 1/4
Please explain. I want to know how you guys approach such problems[/img]
I get D. Although C could be it too, but im guessin D.
-1^k+1 will be even when k is odd.
1/2^k will eventually get so small we don't need to worry about it anymore.
I tried up til k=5. or 1/2^5 ---> 1/32.
When k is 1 we get an answer of 1.5.
The list is as follows:
From this we can see that 1.5-1.25 is .25, then when added the the difference of 1.125-1.0625 we get .3125.
After this u don't really need to add anymore b/c the numbers get so small they are almost irrelevant.
Like I said i didn't add any more past this b/c 1.03125- the next number will yield a small result to add to our current .3125.
So I concluded answer is D.