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For every integer k from 1 to 10, inclusive, the kth term of [#permalink]
03 Jun 2007, 02:27
1
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
55% (hard)
Question Stats:
60% (02:37) correct
40% (01:48) wrong based on 103 sessions
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 in the sequence, then T is
suppose
S=1+1/2+1/4+1/8............................ this is an infinite GP and here
s comes to be S=2(which is max).
Now we are given
S=1/2-1/4+1/8-1/16+...........
here solving for first two terms we get 1/4 i.e .25 means our answer should be greater than .25 as all other terms gives positive in pair of two.
Now the max. value of this expansion will be 1 when all the terms are positive and upto infinite but in this every alternate term is negative thus reducing the sum of expansion to half of 1 that is 1/2(.5) which can be the max. value.
Thus value lies b/w .25 and .50.
suppose S=1+1/2+1/4+1/8............................ this is an infinite GP and here s comes to be S=2(which is max). Now we are given S=1/2-1/4+1/8-1/16+........... here solving for first two terms we get 1/4 i.e .25 means our answer should be greater than .25 as all other terms gives positive in pair of two. Now the max. value of this expansion will be 1 when all the terms are positive and upto infinite but in this every alternate term is negative thus reducing the sum of expansion to half of 1 that is 1/2(.5) which can be the max. value. Thus value lies b/w .25 and .50.
D should be the answer.
Good explanation. Answer is correct. But please remember it is not "infnite G.P." Up to 10 terms only.
For every integer k from 1 to 10, inclusive, the kth term... [#permalink]
04 Aug 2013, 11:05
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 in the sequence, 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
Last edited by Zarrolou on 04 Aug 2013, 11:07, edited 1 time in total.
Re: For every integer k from 1 to 10, inclusive, the kth term... [#permalink]
04 Aug 2013, 11:24
Expert's post
njkhokh 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 in the sequence, 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
From the given sum, T \(= \frac{1}{2}-\frac{1}{2^2}.......-\frac{1}{2^{10}}\)
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