anonymous
  • anonymous
how can this limit be solved??? limit (x->infinit) ( 3^x)/(1*2*3....*x)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
This will go to zero.
anonymous
  • anonymous
yes, I know it will go to zero, but is there an easy way to solve it (I ahve found a long long one)
anonymous
  • anonymous
You can say that every time x increases by 1, you are multiplying the numerator by 3 and multiplying the denominator by a bigger number. So as x goes to infinity, you keep multiplying the numerator by 3 while multiplying the denominator by infinity (essentially)

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anonymous
  • anonymous
ok, is this right? f(x)=3^x/x! for x>3 -> f(x+1)=f(x)*3/x < f(x+1)
anonymous
  • anonymous
anything / a very large number = 0.
anonymous
  • anonymous
that's the simplest answer.

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