Thread: Couple of converge/diverge sequences.. Don't understand

1. Couple of converge/diverge sequences.. Don't understand

For this one I did 3^((5+3n)/n) and I got the sequence converges to the square root of 27 and put that in but I was wrong.

This one I did 2^n/9^n and I got that the sequence converges to 2/9 but I was wrong again.

I don't understand why I am wrong.. Isn't this the correct way to solve it?

2. $\sqrt[n]{{3^{5 + 3n} }} = 27\sqrt[n]{{3^5 }}$

$\dfrac{{2^{n + 6} }}{{9^n }} = 2^6 \left( {\dfrac{2}{9}} \right)^n$

3. As for the 2nd one shouldn't it be diverging?

4. Originally Posted by Reefer
As for the 2nd one shouldn't it be diverging?
No indeed.
What is the limit of $\left( {\frac{2}{9}} \right)^n~?$