kuristar wrote:

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, then T is:

a. greater than 2

b. between 1 and 2

c. between 1/2 and 1

d. between 1/4 and 1/2

e. less than 1/4

i guess

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

(-1)^(k+1)*(1/2^k)

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

2nd term = (-1)^(k+1)*(1/2^k) = -1/4

3rd term = (-1)^(k+1)*(1/2^k) = 1/8

4th term = (-1)^(k+1)*(1/2^k) = -1/16

now we can get every term by multiplying the prededing term by -1/2. so..

5th = 4th term (-1/2) = -1/16 (-1/2) = 1/32

6th = - 1/64

7th = 1/128

8th = -1/256

9th = 1/512

10th = -1/1024

get the sum of every 2 conseqcutive terms

sum of 1st and 2nd term = 1/2 - 1/4 = 1/4

sum of 3rd and 4th term = 1/8 - 1/16 = 1/16

similarly the next term becames = (1/16)(1/4)=1/64

the next term becames = (1/64)(1/4)=1/256

the final term becames = (1/256)(1/4)=1/1024

lets add them all =1/4 +1/16+1/64+1/256+1/1024 = 331/1024

so this value is ====>>>>>

1/4 < 331/1024 < 1/3

it is D.