Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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 \[0<3^n\leq 5^n\]

Answer 5

divide through by \[n5^n\] and use the "squeeze/sandwich" theorem

but it pretty much amounts to the same thing

Answer 6

Thank you that make sense!