The value of $\lim_{n \to \infty} \sum_{r=1}^n \left(\frac{r}{n}\right)^2 \frac{1}{n}$ is equal to
Step-by-Step Solution
Key Concept: Strategic use of substitutions and algebraic manipulation to simplify complex integrals
Using appropriate substitutions and definite integral properties, the integral evaluates to 1. The key is recognizing the structure of the integrand and applying standard techniques.
Correct Answer: 1