1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Geometric series

  1. Jun 24, 2008 #1
    [​IMG]

    [​IMG]


    See above files (one is the question and one is the answer)

    I can to the whole question, other than the last part - for part (f), why are we concerned with the sum to infinity of the series? I am confused as to why this is necessary.


    Any help is appreciated.

    Thanks
     
  2. jcsd
  3. Jun 24, 2008 #2

    tmc

    User Avatar

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Geometric series
  1. Geometric Series (Replies: 7)

  2. Geometric series (Replies: 1)

  3. Geometric Series (Replies: 4)

  4. Geometric series (Replies: 5)

  5. Series (Geometric?) (Replies: 5)

Loading...