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

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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, 04:53

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

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[#permalink]

17 Jul 2007, 10:40

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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17 Jul 2007, 15:13

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.

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Re: geometric progression ? [#permalink]

17 Jul 2007, 20:28

anonymousegmat wrote:

(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.

Re: geometric progression ? [#permalink] 17 Jul 2007, 20:28

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

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

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