anonymous
  • anonymous
How do you determine whether a = 3^(n+2) / 5^n converges or diverges?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
I can't seem to take the limit of it how would you go about doing so
anonymous
  • anonymous
you can rewrite the expression\[(a_n)=\frac{3^{(n+2)}}{5^n}\]
anonymous
  • anonymous
as \[(a_n)=3^2\frac{3^n}{5^n}\]

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anonymous
  • anonymous
you could make the argument that since \[5^n\] increases much "faster" than \[3^n\] as \[n\rightarrow \infty\] and so the the limit is zero or a little more formally set up an inequality like \[0<3^n\leq 5^n\]
anonymous
  • anonymous
divide through by \[n5^n\] and use the "squeeze/sandwich" theorem but it pretty much amounts to the same thing
anonymous
  • anonymous
Thank you that make sense!

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