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Puzzle: one over one plus one over one plus…

April 2, 2007 pm30 6:59 pm

A month ago Dave Marain ran a discussion of \sqrt{2 + \sqrt{2 + \sqrt{2 + \dotsb}}} over here.

I know this one has been done many many times before. But he generated a nice discussion.

In the same vein, what is the value of \frac{1}{1+\frac{1}{1 + \frac{1}{1 + \dotsb}}} ?

Once again I am preparing separate comment places for

  1. methods of solution and
  2. different versions of the problem, suitable for older/younger more advanced/less advanced students.

Questions belong in the comment space, right here.

What makes these two problems so similar?

One Comment leave one →
  1. April 2, 2007 pm30 11:57 pm 11:57 pm

    The continuous fraction is the Golden Ratio? Or wait, there’s a leading 1 missing. So it’s the reciprocal of the GR?

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