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Simplifying limit help

  • Thread starter cauchy21
  • Start date
  • #1
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Homework Statement



(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

Homework Equations





The Attempt at a Solution


I tried to use Limit theorems but nothing happened.
 
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Answers and Replies

  • #2
jbunniii
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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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