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

[mxyplizk]

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...

 

[Char. Limit]

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...

 

[Char. Limit]

Oh, I remember.

Take a look at the denominator. The denominator CONTAINS B, as long as the series is infinite.

 

[mxyplizk]

Thanks for your help!

 

[Char. Limit]

No problem.