Let $f(x) = \frac{2e^{2x}}{e^{2x} + e}$. Find the value of $\sum_{k=1}^{99} f\left(\frac{k}{100}\right)$.
Step-by-Step Solution
Key Concept: Show that $f(x) + f(1-x) = 2$. Pair the 99 terms so that each pair sums to 2, and handle the middle term separately.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 99