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Homework Help: Geometric series

  1. Jun 24, 2008 #1
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jun 24, 2008 #2

    tmc

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    The sum that is done here is not the sum of the areas of every S_i; it is the sum whose result is the area of S_n itself. Look at A_3 in part (e), it is given as
    A_3 = a^2 + 4a^2/9 + 4a^2/27
    From this, you could guess that
    A_4 = a^2 + 4a^2/9 + 4a^2/27 + 4a^2/81
    And so on, such that A_n is such a sum. Every new term in the sum is the area of the extra little squares tacked onto the shape.
     
  4. Jun 24, 2008 #3
    Hi, I understand that it is a geometric series, I was concerned with part (f). My question is why use the sum to infinity?

    Thanks
     
  5. Jun 24, 2008 #4

    tiny-tim

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    Hi nokia8650! :smile:

    Because you want sup{Sn}, and the sequence is increasing, so you want S. :smile:
     
  6. Jun 24, 2008 #5
    Thanks. The question says the sum to n, so shouldnt the equation be the sum ton, not the sum to inifnity?

    Thanks
     
  7. Jun 24, 2008 #6

    tiny-tim

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    Hi nokia8650! :smile:
    erm … no, it doesn't … it says "Find the smallest value of the constant S such that the area of Sn < S, for all values of n."

    So you want sup{area of Sn}, which is the "area of S". :smile:
     
  8. Jun 24, 2008 #7
    Thanks for the help. Its the wording of the question that is confusing me! So the question asks for the value of a constant which is greater than the area of the "final" square?

    Thanks
     
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