ok i have this problem in the textbook where An= 3^(n+2)/5^n and i am suppose to determine whether it converges or diverges and if it convergies i have to find the limit... any ideals how to do this?

2. Originally Posted by Krebs
ok i have this problem in the textbook where An= 3^(n+2)/5^n and i am suppose to determine whether it converges or diverges and if it convergies i have to find the limit... any ideals how to do this?

$\displaystyle A_n = \frac{3^n 3^2}{5^n} = 9 \left( \frac{3}{5} \right)^n$. To show it converges show (i) it's decreasing and (ii) bounded below by 0.

3. Originally Posted by danny arrigo

$\displaystyle A_n = \frac{3^n 3^2}{5^n} = 9 \left( \frac{3}{5} \right)^n$. To show it converges show (i) it's decreasing and (ii) bounded below by 0.

ok so that means that as n approaches infinity An approaches 0 since An is getting smaller and smaller as n gets larger? and thank you for your help

4. Originally Posted by Krebs
ok so that means that as n approaches infinity An approaches 0 since An is getting smaller and smaller as n gets larger? and thank you for your help
Yes. More formally you want to show (for decreasing)

$\displaystyle A_{n+1} < A_n$

I think that $\displaystyle A_n >0$ is obvious.