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Quiz: Infinite Continued fractions

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At the SouthWest Fox speaker dinner we were talking about continued (or infinite) fractions.

I posed this question:

What does this expression evaluate to?

       1 + 1

                  _________

                   1 + 1

                          ________

                           1 + 1

  _______

                                  1 + 1

                                         ______

                                          1 + 1

                                              …

Clue: It’s adding some positive value to 1, so it must be larger than one. The thing it’s adding is the reciprocal of some number larger than 1 so….

Comments

  • Anonymous
    November 02, 2005
    The golden ratio : 1.618034
  • Anonymous
    November 02, 2005
    x = 1 + 1/x
    ==>
    x = (1+sqrt(5))/2
    ==> 1.618034
  • Anonymous
    November 02, 2005
    1.618034 or -0.618034 (the golden ratio is an irrational number)
  • Anonymous
    November 02, 2005
    Raj:

    Never assume that the fact that the expression contains sqrt(5) somewhere in it implies that both positive and negative roots are correct for the answer.

    The answer must be positive in this case, and so you cannot take the negative root.
  • Anonymous
    November 02, 2005
    The comment has been removed