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by swativerma1103 » Sun Jul 22, 2012 6:00 am
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
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by eagleeye » Sun Jul 22, 2012 8:13 am
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.)
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by swativerma1103 » Sun Jul 22, 2012 10:49 am
thanks..can you please share the link for posting such questions, as I have other queries also.
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by eagleeye » Sun Jul 22, 2012 11:49 am
swativerma1103 wrote:thanks..can you please share the link for posting such questions, as I have other queries also.
For PS questions use
https://www.beatthegmat.com/problem-solving-f6.html

For DS questions use
https://www.beatthegmat.com/data-sufficiency-f7.html

For others, just browse through the site.

Cheers!
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by AJWILL » Sun Jul 22, 2012 12:28 pm
This is my doubt too..

but i didnt understand the explanation..

can someone please elaborate on how is the first term 1/2?

coz its written k=integer not necessarily a positive integer!!
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by eagleeye » Sun Jul 22, 2012 12:42 pm
AJWILL wrote:This is my doubt too..

but i didnt understand the explanation..

can someone please elaborate on how is the first term 1/2?

coz its written k=integer not necessarily a positive integer!!
Its a gmatprep question that i did in the mock exam. The full question reads for k=1 to 10........

If k was given as only an integer, we'd have no solution.
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