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E as an average

  1. Mar 13, 2007 #1
    How can one generate the sequence of whole numbers x and y which converge upon the equality

    (2x+3y)/(x+y) = e

    ?
     
  2. jcsd
  3. Mar 14, 2007 #2

    AKG

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    (2x+3y)/(x+y) = e gives x/y = (e-3)/(2-e), so it suffices to find a sequence of rationals which converges to (e-3)/(2-e). If the decimal expansion of (e-3)/(2-e) is given, then we can just set y = 1, 10, 100, 1000, 10000, ... and make the obvious choice for x.
     
  4. Mar 14, 2007 #3
    Same as above- except use continued fractions for x/y=(e-3)/(2-e)
     
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