calculus - Compute $lim_{n to infty} frac{1}{n} ln(3^frac{n}{1}+3^frac{n}{2}+cdots+3^frac{n}{n})$

$$\lim_{n \to \infty} \frac{1}{n} \cdot\ln(3^\frac{n}{1}+3^\frac{n}{2}+\cdots+3^\frac{n}{n})$$
I tried to apply the squeeze theorem, but I can't manage to solve it.

Answer

The squeeze theorem is a good idea.

$$\ln(3^n)\leq \ln(3^\frac{n}{1}+3^\frac{n}{2}+\cdots+3^\frac{n}{n}) \leq \ln(n\cdot3^n)$$