Functions
Functional Series
JEE Main 2021
Grade 12
Question:
Given $f(x) = \frac{5^x}{5^x + 5}$, the value of $f\left(\frac{1}{20}\right) + f\left(\frac{2}{20}\right) + \dots + f\left(\frac{39}{20}\right)$ is:
(1) $\frac{41}{2}$
(2) $20$
(3) $\frac{39}{2}$
(4) $19$
Step-by-Step Solution
Key Concept: Verify that $f(x) + f(2 - x) = 1$. Pair the 39 terms into groups that sum to 1, then handle the unpaired middle term $f(1)$ separately.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)