Irrational sequence that converges to a rational limit

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Homework Help Overview

The discussion revolves around the search for an irrational sequence that converges to a rational limit, specifically exploring examples and suggestions related to this concept.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the possibility of constructing an irrational sequence that converges to 0, with suggestions involving irrational numbers in the numerator of a fraction. There is also mention of avoiding certain types of irrational numbers.

Discussion Status

Several participants have offered suggestions and examples, with some expressing gratitude for the ideas shared. The conversation appears to be productive, with multiple approaches being explored without a clear consensus on a single solution.

Contextual Notes

Participants have noted preferences regarding the types of irrational numbers to use, indicating a desire to avoid certain categories like transcendental numbers.

cnwilson2010
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Hi. I found some rational sequences that converge to irrational limits, but am not having any luck going the other direction, i.e., an irrational sequence that converges to a rational limit. Any suggestions?
 
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Can you find an irrational sequence that converges to 0? Something like [itex]\frac{1}{n}[/itex] but with an irrational number in the numerator?
 
Thank you.

How about 1/n(2(1/2))?
 
cnwilson2010 said:
Thank you.

How about 1/n(2(1/2))?

Yes, that sounds good! :smile:
 
You can also use a commonly known irrational number (e.g. pi or e) and do something similar.
 
Didn't want to be oddly transcendental or anything, so I was trying to stay away from those, but found out later they would have been fine. So thank you for that.
 

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