How to determine the limit of a quotient containing exponents involving n? I'm trying to work out the limit of the following:
$$\frac{n2^n}{(n+1)3^n + n^7}$$
but I'm having a hard time applying the algebra of limits to the $2^n$ and $3^n$ terms. Can anyone point me in the right direction please?
Thanks

We have $\frac{n(2^{n})}{(n+1)3^{n} + n^{7}}$ is always greater than $0$ for positive $n$. On the other hand, $\frac{n(2^{n})}{(n+1)3^{n} + n^{7}} \leq \frac{2^{n}}{3^{n}}$ which goes to $0$ as n goes to infinity. Thus, the limit should be $0$.
