Mathematics

This is a Riemann sum in disguise—you're looking at a sum that approximates an integral as $n \to \infty$. Recognize that $\frac{3}{n}$ is the width of each rectangle, and $\sqrt{1+\frac{3i}{n}}$ is the height evaluated at partition points. Rewrite the sum to identify the integrand and limits of integration, then evaluate the resulting definite integral to find the exact value—which will be an interval endpoint.

This is a Riemann sum in disguise—you're looking at a sum that approximates an integral as $n \to \infty$. Recognize that $\frac{3}{n}$ is the width of each rectangle, and $\sqrt{1+\frac{3i}{n}}$ is the height evaluated at partition points. Rewrite the sum to identify the integrand and limits of integration, then evaluate the resulting definite integral to find the exact value—which will be an interval endpoint.