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I need help with sequences

  1. Mar 26, 2013 #1
    1. Finding the limit of the sequence:

    { an } = 5n^(2) / (n^(2) + 2)





    2. Relevant equations



    3. what i did was :

    lim as (n -> Infinity) of function [5n^(2) / (n^(2) + 2)]


    Then factored out the constant:


    5{lim as (n -> Infinity) of function [n^(2) / (n^(2) + 2)]}

    so at this point i plug in infinity for the function
    and this is where i need help.

    how is it of the indeterminate form infinity/infinity.

    when i plug it in i get infinity / (infinity + 2)

    so isn't it just infinity?
     
    Last edited by a moderator: Mar 26, 2013
  2. jcsd
  3. Mar 26, 2013 #2

    tiny-tim

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    hi physics=world! :smile:
    an indeterminate form is exactly that … indeterminate!

    ie, you can't give it a value

    ∞/∞ can be 0 or ∞ or anything in between

    hint: divide top and bottom by n2 :wink:
     
  4. Mar 26, 2013 #3
    hmm it works when i use your hint.. dividing be n^2

    but i just can't understand why it is of indeterminate form infinity/infinity

    when i plug it in i get infinity / (infinity + 2) which would equal [infinity / 2] ?

    so would that be just infinity?

    im trying to understand it so i can use L'Hospitals rule.
     
  5. Mar 26, 2013 #4

    tiny-tim

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    hi physics=world! :smile:

    i don't understand this line …
    where did the ∞ on the bottom go? :confused:

    ∞ is lot larger than 2 (!), so why are you ignoring it, instead of ignoring the 2 ? :wink:
     
  6. Mar 26, 2013 #5

    Ibix

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    The aim with limits is to avoid writing [itex]n=\infty[/itex] by thinking about what happens as n gets larger and larger. Some terms become less and less significant as n grows. You describe them as 'negligible' and drop them and, if the limit is nice, the answer drops out.

    Which term becomes negligible?
     
  7. Mar 26, 2013 #6
    what i was thinking was that infinity was like 0. so i just thought it would be infinity over 2.

    so, the 2 is supposed to be ignored?
     
  8. Mar 26, 2013 #7

    tiny-tim

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    no!!!

    ∞ is as different from 0 as you can get …

    a reasonably safe rule is that anything you can do with 0, you can't do with ∞ ! :smile:
    yup! :biggrin:
     
  9. Mar 26, 2013 #8
    so for example if it was say 5 / infinity

    would the answer be zero? or infinity? or undefined?
     
  10. Mar 26, 2013 #9

    tiny-tim

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    only ∞/∞ is undefined

    anything-else/∞ is 0 (because anything-else is negligible compared with ∞) :wink:
     
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