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Proof without words: Geometric series

  1. Apr 29, 2012 #1
    On this website http://www.albany.edu/~bd445/Eco_466Y/Slides/Infinite_Geometric_Sum,_Proof_Without_Words.pdf [Broken] there is a "proof without words" of the sum of the infinite geometric series. However, I don't understand what makes the proof valid. In what order were the constructions done etc.? What were the arguments of the proof?

    I am referring to the very first picture with the similar triangles.

    BiP
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Apr 29, 2012 #2

    tiny-tim

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    Hi Bipolarity! :smile:

    Triangle PQR is similar to triangle TSP.

    So the two tans are the same. :wink:
     
  4. Apr 29, 2012 #3
    I get that part, but I don't understand how you can construct the line that is equal to the geometric sum.

    BiP
     
  5. Apr 29, 2012 #4

    tiny-tim

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    oh i see! :smile:

    those diminishing quadrilaterals are similar to each other …

    each has two sides the same, and one side r times those two :wink:
     
  6. Apr 29, 2012 #5
    I don't understand how the quadrilaterals were constructed in the first place?

    BiP
     
  7. Apr 29, 2012 #6

    tiny-tim

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    each quadrilateral is stuck onto the previous one, so they're each reduced by r :wink:
     
  8. Apr 29, 2012 #7
    I get it now. Thanks.

    BiP
     
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