Problem Solving

For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1) ^k+1 times (1/2^k). If T is the sum of the first 10 terms in the sequence, then T is which fo the following?

a. greater than 2
b. between 1 & 2
c. between 1/2 & 1
d. between 1/4 & 1/2
e. less than 1/4

Answer is d.

Thanks for your help!

Start with if k=1 (as k must be between 1 and 10), the first term of the sequence is (-1)^1+1 * (1/2^1) = 1/2. The next term if k=2 is (-1)^1+2 * (1/2^2) = -1/4.

Similarly, the next term(s) to k=10 will yield the pattern of terms: 1/8, -1/16, 1/32, -1/64 etc. So it is apparent that T (the sum of the first 10 terms in the sequence) is between 1/4 and 1/2, since 1/2-1/4+1/8-1/16...

Hope it helps.

Ohhhhhh! Thank you. I didn't recognize the pattern.