Series proof: 1/1+(1/1+(1/1+(1/1+ what does it equal?

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Homework Help Overview

The problem involves evaluating the infinite series defined as B = 1/(1 + (1/1 + (1/1 + (1/1 + ...))). The context is primarily conceptual, focusing on the behavior of this recursive expression.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to determine the value of B and questions whether it converges to 0. They provide a sequence of calculations to explore this idea. Other participants suggest algebraic manipulation and point out that the denominator includes B itself, indicating a recursive relationship.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to understand the series. Some guidance has been offered regarding algebraic manipulation, but no consensus has been reached on the value of B.

Contextual Notes

The problem is framed as a conceptual question without specific equations provided, which may limit the approaches discussed.

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Homework Statement


B=1/(1+(1/1+(1/1+(1/1+(1/1+...

what does B equal?


Homework Equations



I don't believe there are any...it's a conceptual question.


The Attempt at a Solution


Would it converge to 0? My reasoning was that if 1/(1+1)=1/2, and then 1/(1+1/2)=1/(3/2)=2/3, and 1/(1+(2/3))=1/(5/3)=3/5, and 1/(1+(5/3))=1/(8/3)=3/8, etc...
 
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There's usually a way to algebraically manipulate this into a quadratic or similar problem. Have you tried that?

I can't quite remember how it goes, though...
 
Oh, I remember.

Take a look at the denominator. The denominator CONTAINS B, as long as the series is infinite.
 
Thanks for your help!
 
No problem.
 

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