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Limit help

  1. Apr 18, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex] X \geq Y > 0, find \lim_{n \to \infty} \left(\frac{2X^n + 7Y^n}{2}\right)^{1/n}
    [/tex]
    2. Relevant equations



    3. The attempt at a solution
    I'm not really sure how to do it, but i guess I need to use the fact that [tex] \frac{Y}{X} \leq 1 [/tex], and so [tex] \lim_{n \to \infty} \left(\frac{Y}{X}\right)^n = 0. [/tex]
    Thanks for your help.
     
  2. jcsd
  3. Apr 18, 2009 #2

    Cyosis

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    Multiply the argument by [tex]\frac{X^n}{X^n}[/tex] then take the [tex]X^n[/tex] out of the brackets.
     
  4. Apr 18, 2009 #3
    [tex] \lim_{n \to \infty} X \left( 1 + \left( \frac{7Y}{2X} \right)^n \right)^{1/n} [/tex]
    But I'm still stuck on how to procceed, if you could help.
     
  5. Apr 18, 2009 #4

    Cyosis

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    There is one mistake, 7/2 should not be within the brackets. Now take X in front of the limit and use [tex] \frac{Y}{X} \leq 1 \Rightarrow \lim_{n \to \infty} \left(\frac{Y}{X}\right)^n = 0[/tex].
     
  6. Apr 18, 2009 #5
    Oh right.. So its limit is X.
    Thanks :-D
     
  7. Apr 18, 2009 #6

    Cyosis

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    That's right!
     
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