Question

Evaluate the following limit: $ \lim_{n \to \infty} \prod_{r=3}^n \frac{r^3 - 8}{r^3 + 8} $.

• A. \( \frac{2}{7} \)
• B. \( \frac{3}{7} \)
• C. \( \frac{4}{7} \)
• D. \( \frac{6}{7} \)

Hint:

For infinite product limits, identify factors that cancel and apply asymptotic analysis for large \( n \).