Making a geometric series that converges to a number

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Homework Help Overview

The discussion revolves around creating a geometric series that converges to a specific number, such as 2. Participants express confusion about the process of working backwards to formulate such a series.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants inquire about the properties of geometric series and their sums, with some suggesting the use of the formula for the sum to infinity. Others propose considering simpler series that sum to a different number and exploring the effects of scaling.

Discussion Status

The discussion is ongoing, with participants sharing thoughts on how to approach the problem. Some guidance has been offered regarding the sum of geometric series, but no consensus or definitive solution has emerged yet.

Contextual Notes

Participants are working within the constraints of homework guidelines, which may limit the types of examples or methods they can explore.

jdawg
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Homework Statement



How do you come up with a geometric series that converges to a number like 2?
I'm kind of confused on how to work backwards through the problem. If someone could provide me with an example, that would be great!

Homework Equations





The Attempt at a Solution

 
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jdawg said:

Homework Statement



How do you come up with a geometric series that converges to a number like 2?
I'm kind of confused on how to work backwards through the problem. If someone could provide me with an example, that would be great!

Homework Equations





The Attempt at a Solution


What do you know about the sum of a geometric series? It's probably not that big of a backward step.
 
You use the formula for the sum to infinity.
 
jdawg said:

Homework Statement



How do you come up with a geometric series that converges to a number like 2?
I'm kind of confused on how to work backwards through the problem. If someone could provide me with an example, that would be great!

Homework Equations





The Attempt at a Solution


Can you think of a geometric series that sums to 1? What happens if you multiply every term by 2?
 

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