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Simplifying limit help

  1. Mar 13, 2010 #1
    1. The problem statement, all variables and given/known data

    (a) [tex]lim_{n\rightarrow\infty}[/tex] ([tex]\sqrt{(n + a)(n + b)} - n)[/tex] where a, b > 0
    (b)[tex]lim _{n\rightarrow\infty}[/tex] (n!)1/n2

    2. Relevant equations

    3. The attempt at a solution
    I tried to use Limit theorems but nothing happened.
    Last edited by a moderator: Aug 2, 2014
  2. jcsd
  3. Mar 13, 2010 #2


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    Re: Limits

    For part (a), try multiplying by

    [tex]\frac{\sqrt{(n+a)(n+b)} + n}{\sqrt{(n+a)(n+b)} + n} = 1[/tex]

    and simplifying until you can evaluate the limit term-by-term.

    For part (b), try defining

    [tex]y_n = \log x_n[/tex]

    and see if you can find

    [tex]\lim_{n\rightarrow \infty} y_n[/tex]

    and if so, can you relate that to

    [tex]\lim_{n\rightarrow \infty} x_n[/tex]?
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