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

  • Thread starter mxyplizk
  • Start date
  • #1
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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...
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
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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...
 
  • #3
Char. Limit
Gold Member
1,204
14
Oh, I remember.

Take a look at the denominator. The denominator CONTAINS B, as long as the series is infinite.
 
  • #4
8
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Thanks for your help!
 
  • #5
Char. Limit
Gold Member
1,204
14
No problem.
 

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