anonymous
  • anonymous
Can someone explain why An = (2^n)/[3^(n+1)] has a limit of 0. I'm missing something algebraically, I guess.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
A limit of 0 when?
anonymous
  • anonymous
as n goes to infinity?
anonymous
  • anonymous
What gets bigger faster, 2^n or 3^n?

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anonymous
  • anonymous
3^n
anonymous
  • anonymous
So you'll get a number very very very large on the bottom sooner than you get one on the top, so it'll approach (something)/∞ before ∞/(something) or ∞/∞.
anonymous
  • anonymous
There are more rigorous mathematical ways to show that, but do you understand the reasoning?
anonymous
  • anonymous
I see. I mean, I understand it conceptually. Just not sure how I "show" that when I'm writing things out. "infinity/infinity" for work shown?
anonymous
  • anonymous
And if it is infinity over infinity, then how would that converge to 0?
anonymous
  • anonymous
Are you familiar with calculus derivatives and L'Hopital's rule?

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