swativerma1103 wrote:for every integer inclusive the kth term of a certain sequence given by (-1)^(k+1),(1/2^k), T is the sum of first 10 terms then T is
a) greater than 2
b) between 1 & 2
c) between 1/2 & 1
d) between1/4 & 1/2
e) less than 1/4
Hi swativerma1103: You've posted this question in the wrong part of the forum. Anyway, here's the solution.
1st term = +1/2
2nd term = -1/4
3rd term = +1/8
4th term = -1/16
.
.
.
9th term = +1/2^9
10th term = -1/2^10.
Add the terms in pairs = (1/2-1/4) + (1/8-16) +......(1/512-1/1024)
= 1/4 + 1/16 + 1/64 + 1/256 + 1/1024.
Clearly this is greater than 1/4 but less than 1/2 (as each consecutive term after 1/4 keeps decreasing by a factor of 4).
D is correct.
Cheers!
(Alternatively you could show that the sum is less than 1/2 by adding the sum of infinite series
S = 1/4 + 1/(4^2) + 1/(4^3) + ......... = 1/4*(1/(1-1/4)) = 1/4 *4/3 = 1/3. Clearly sum of infinite terms is 1/3. so our sum is definitely less than 1/2.)
