1. **State the problem:** Find the limit as $n$ approaches positive infinity of the expression $$\frac{3n^2 + 7n + 1}{3n^2 - n + 2}$$. 2. **Recall the rule for limits of rational functions at infinity:** When the degrees of the numerator and denominator polynomials are the same, the limit is the ratio of the leading coefficients. 3. **Identify the leading terms:** The highest degree term in numerator is $3n^2$ and in denominator is $3n^2$. 4. **Divide numerator and denominator by $n^2$ to simplify:** $$\lim_{n \to +\infty} \frac{3n^2 + 7n + 1}{3n^2 - n + 2} = \lim_{n \to +\infty} \frac{3 + \frac{7}{n} + \frac{1}{n^2}}{3 - \frac{1}{n} + \frac{2}{n^2}}$$ 5. **Evaluate the limit by substituting $n \to +\infty$:** Terms with $\frac{1}{n}$ and $\frac{1}{n^2}$ go to zero. $$= \frac{3 + 0 + 0}{3 - 0 + 0} = \frac{3}{3} = 1$$ 6. **Final answer:** $$\boxed{1}$$