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Sum of Infinite Series

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the limit of the sum of:

    y = (2n + 3n) / 4n


    3. The attempt at a solution

    as n-> infinity, y approaches 0. I don't know where to proceed from here.
     
  2. jcsd
  3. Oct 10, 2009 #2

    Dick

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    It's 2^n/4^n+3^n/4^n=(2/4)^n+(3/4)^n. It's two separate geometric series. Can you deal with those?
     
  4. Oct 11, 2009 #3
    Ya I got that but I don't know how to find the sum of an infinite geometric series
     
  5. Oct 11, 2009 #4

    Dick

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    That's regrettable. Then you should probably try to look it up in your text or online. It's pretty basic.
     
  6. Oct 11, 2009 #5
    Oh sorry I'm stupid, I remembered how haha.

    Since you're here I also have another hard one.

    A circle is inscribed in a triangle, a square is inscribed in that circle, a circle is inscribed is that square, a pentagon is inscribed in that circle, the trend continues with the degree going up.

    How do I proceed to solve this quesiton? I need to find t he sum of the limit
     
  7. Oct 11, 2009 #6

    Dick

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    The first one wasn't hard. That one probably is. What are to trying to find the sum or the limit of? The areas, or the perimeters or the radii, or what? Not that I know the answer. But your question isn't even clear.
     
  8. Oct 11, 2009 #7
    The limit of the sum of the area. Sorry forgot that detail.
     
  9. Oct 11, 2009 #8

    Dick

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    The sum of the areas of ALL of the geometric figures? I think it's pretty likely it diverges. Mostly gut feeling. Is this for a class, or is this your own creation? It's way out of scale with the difficulty of your first problem.
     
  10. Oct 11, 2009 #9
    It was a bonus question on our test yesterday. Yup we need the limit of the sum of all of the areas. I know that the areas of the figures approach to 0 thats easy.
     
  11. Oct 11, 2009 #10

    Dick

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    How do you know the areas approach zero? Sure, they decrease. But that doesn't convince me that they approach zero. Do you know this has a simple solution? Because I'm sure not seeing it.
     
  12. Oct 11, 2009 #11
    Area can't be negative, and area decreases, it has to approach 0. Right?
     
  13. Oct 11, 2009 #12

    Dick

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    Nope. 1+1/n is a positive decreasing sequence but it doesn't approach 0. It approaches 1.
     
  14. Oct 11, 2009 #13
    Sorry where do you get 1+ 1/n?
     
  15. Oct 11, 2009 #14

    Dick

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    It's just an example of a sequence that decreases but doesn't approach zero.
     
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