1. The problem is to find the limit: $$\lim_{n \to \infty} \frac{1}{\ln n}$$. 2. Recall that the natural logarithm function $\ln n$ increases without bound as $n$ approaches infinity, but it does so very slowly. 3. Since $\ln n \to \infty$ as $n \to \infty$, the denominator of the fraction $\frac{1}{\ln n}$ grows without bound. 4. When the denominator of a fraction grows without bound and the numerator is constant (1), the fraction approaches zero. 5. Therefore, $$\lim_{n \to \infty} \frac{1}{\ln n} = 0$$. 6. In simple terms, as $n$ gets very large, $\ln n$ becomes very large, making $\frac{1}{\ln n}$ very small, approaching zero.