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

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CEO
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1/2 + (1/2)^2 + (1/2)^3 .....(1/2)^20 is between 1/2 and 2/3 [#permalink]

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New post 06 Nov 2007, 13:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

1/2 + (1/2)^2 + (1/2)^3 .....(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



Not sure what concept this question is testing...
CEO
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Re: exponents [#permalink]

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New post 06 Nov 2007, 13:54
bmwhype2 wrote:
1/2 + (1/2)^2 + (1/2)^3 .....(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



Not sure what concept this question is testing...


okay nevermind. i figured it out.

the "concept" is the equation keeps adding increasingly negligible fractions as the exponents rise and the sum approaches 1. this is very similar to how limits work as they approach 0 in calculus.
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New post 06 Nov 2007, 14:02
Actually, I don't think it ever approaches 1. But you do have the concept right. I think its between 3/4 - 9/10.

Basically this is as far as you need to take it...

1/2 + 1/4 + 1/8 + 1/64 (where it becomes negligible)

adding the totals you get:

3/4, then 7/8, then negligible addition from there.
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New post 06 Nov 2007, 14:17
emoryhopeful wrote:
Actually, I don't think it ever approaches 1. But you do have the concept right. I think its between 3/4 - 9/10.

Basically this is as far as you need to take it...

1/2 + 1/4 + 1/8 + 1/64 (where it becomes negligible)

adding the totals you get:

3/4, then 7/8, then negligible addition from there.


yea. i should have clarified that. the limits never reach zero in calc, or at least that's what i remember of calculus in college.
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New post 06 Nov 2007, 14:23
gowani wrote:
is the OA C?


OA is D.

in C 9/10 is .90 which is less than 1. however, the sum breaks that upper bound and is constrained by 1. only D satsifies the concept.
  [#permalink] 06 Nov 2007, 14:23
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