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# 1/2 + (1/2)^2.... + (1/2)^20 is between: 1/2 and 2/3 2/3 and

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Senior Manager
Joined: 14 Jun 2007
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1/2 + (1/2)^2.... + (1/2)^20 is between: 1/2 and 2/3 2/3 and [#permalink]  17 Jul 2007, 03:53
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
Senior Manager
Joined: 03 Jun 2007
Posts: 384
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Kudos [?]: 10 [0], given: 0

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
Director
Joined: 26 Feb 2006
Posts: 905
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Kudos [?]: 52 [0], given: 0

dahcrap wrote:
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

is it (sum) = a (1 - r^n) / (1 - r)
= [1/2 {1 - (1/2)^20}] / [1 - 1/2]
= 1 approxxxxxxxxxxxxxx.
Manager
Joined: 07 Feb 2007
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Re: geometric progression ? [#permalink]  17 Jul 2007, 19:28
anonymousegmat wrote:
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

(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
Re: geometric progression ?   [#permalink] 17 Jul 2007, 19:28
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