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Prove direct from definition

  1. May 19, 2009 #1
    let an = [tex]\frac{(2n+1)}{(3n+7)}[/tex]. Prove direct from definition that an[tex]\rightarrow2/3[/tex].

    Any help would be appreciated.
    Cheers
     
  2. jcsd
  3. May 19, 2009 #2

    tiny-tim

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    ok … first step in a question like this is …

    what is the definition of the statement "lim((2n+ 1)/(3n+7)) = 2/3"? :smile:
     
  4. May 19, 2009 #3
    Here's an idea... as long as n isn't zero, the following two things are the same:

    (2n+1)/(3n+7) = [(2n)(1+1/2n)]/[(3n)(1+7/3n)]

    What happens as the n's get bigger and bigger to the terms 1/2n and 7/3n?
     
  5. May 19, 2009 #4

    HallsofIvy

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    That's the simplest way of finding the limit but it doesn't "prove from the definition".
     
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