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anonymousegmat
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1/2 + (1/2)^2.... + (1/2)^20 is between: 1/2 and 2/3 2/3 and 17 Jul 2007, 04:53
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1/2 + (1/2)^2.... + (1/2)^20 is between:


1/2 and 2/3
2/3 and 3/4
3/4 and 9/10
9/10 and 10/9
10/9 and 3/2



this is from one of the challenges, and the explanations sucks. it says to imagine a piece of string being cut in half 20 times over... so therefore it will be less than one but close to one. um.. OK, i'd rather be able to solve to problem mathematically.

i am assuming this is a candidate for geometric progression... could someone please explain how to use it



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dahcrap
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1/2 + (1/2)^2.... + (1/2)^20 is between: 1/2 and 2/3 2/3 and 17 Jul 2007, 10:40
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I simply approximated it by using the GP formula for infinite series where Sum = a/(1-r) Here a = 1/2 and r =1/2
So we get approximately 1.
So I guess the answer is D. I forgot the formula for a non infinite series though
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Himalayan
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1/2 + (1/2)^2.... + (1/2)^20 is between: 1/2 and 2/3 2/3 and 17 Jul 2007, 15:13
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dahcrap
I simply approximated it by using the GP formula for infinite series where Sum = a/(1-r) Here a = 1/2 and r =1/2
So we get approximately 1.

So I guess the answer is D. I forgot the formula for a non infinite series though
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is it (sum) = a (1 - r^n) / (1 - r)
= [1/2 {1 - (1/2)^20}] / [1 - 1/2]
= 1 approxxxxxxxxxxxxxx.
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wudy
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1/2 + (1/2)^2.... + (1/2)^20 is between: 1/2 and 2/3 2/3 and 17 Jul 2007, 20:28
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anonymousegmat
1/2 + (1/2)^2.... + (1/2)^20 is between:


1/2 and 2/3
2/3 and 3/4
3/4 and 9/10
9/10 and 10/9
10/9 and 3/2



this is from one of the challenges, and the explanations sucks. it says to imagine a piece of string being cut in half 20 times over... so therefore it will be less than one but close to one. um.. OK, i'd rather be able to solve to problem mathematically.

i am assuming this is a candidate for geometric progression... could someone please explain how to use it
Show more


(1/2)^1 = 1- (1/2)^1
(1/2)^2 = 1/2 -(1/2)^2
...
(1/2)^20 = (1/2)^19-(1/2)^20

Add all the above equations together.
1/2 + (1/2)^2.... + (1/2)^20=1-(1/2)^20
Therefore, D is the answer.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!