1. **Problem Statement:** Find the limit of the sequence $$a_n = \frac{2n + 1}{n}$$ as $$n \to \infty$$. 2. **Formula and Rules:** To find the limit of a rational sequence as $$n$$ approaches infinity, divide numerator and denominator by the highest power of $$n$$ in the denominator. 3. **Step-by-step Solution:** $$\lim_{n \to \infty} \frac{2n + 1}{n} = \lim_{n \to \infty} \frac{\frac{2n}{n} + \frac{1}{n}}{\frac{n}{n}} = \lim_{n \to \infty} \frac{2 + \frac{1}{n}}{1}$$ 4. As $$n \to \infty$$, $$\frac{1}{n} \to 0$$, so: $$\lim_{n \to \infty} \frac{2 + \frac{1}{n}}{1} = 2 + 0 = 2$$ 5. **Final Answer:** $$\boxed{2}$$