JEE PYQ: Functions Question 10
Question 10 - 2021 (25 Feb Shift 2)
A function $f(x)$ is given by $f(x) = \frac{5^x}{5^x + 5}$, then the sum of the series $f\left(\frac{1}{20}\right) + f\left(\frac{2}{20}\right) + f\left(\frac{3}{20}\right) + \cdots + f\left(\frac{39}{20}\right)$ is equal to:
(1) $\frac{19}{2}$
(2) $\frac{49}{2}$
(3) $\frac{29}{2}$
(4) $\frac{39}{2}$
Type: MCQ
Show Answer
Answer: (3) $\frac{29}{2}$
Solution
$f(x) + f(2-x) = 1$
19 pairs summing to 1, plus $f(1) = \frac{1}{2}$
Sum $= 19 + \frac{1}{2} = \frac{39}{2}$
BETA
