Question

The limit \( \lim_{n \to \infty} \left[ \sec^2 \frac{\pi}{4n} + \sec^2 \frac{2\pi}{4n} + \dots + \sec^2 \frac{n\pi}{4n} \right] \) is equal to

• A. \( \frac{4}{\pi} \)
• B. \( \frac{2}{\pi} \)
• C. \( \frac{5}{\pi} \)
• D. \( \frac{3}{\pi} \)

Hint:

For sums of trigonometric functions with small angles, approximate the function using a series expansion and apply summation formulas to find the result.

Answer 1

The Correct Option is A