## anonymous 5 years ago How do you determine whether a = 3^(n+2) / 5^n converges or diverges?

1. anonymous

I can't seem to take the limit of it how would you go about doing so

2. anonymous

you can rewrite the expression$(a_n)=\frac{3^{(n+2)}}{5^n}$

3. anonymous

as $(a_n)=3^2\frac{3^n}{5^n}$

4. 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 $0<3^n\leq 5^n$

5. anonymous

divide through by $n5^n$ and use the "squeeze/sandwich" theorem but it pretty much amounts to the same thing

6. anonymous

Thank you that make sense!