A function f(x) = 5^x / (5^x + 5) then...

JEE MAIN 2021

25-02-2021 S2

Question

A function $f(x)$ is given by $f(x)=\frac{5^x}{5^x+5}$, then the sum of the series $$ f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+f\left(\frac{3}{20}\right)+\ldots \ldots+f\left(\frac{39}{20}\right) $$ is equal to:

Select the correct option:

$\frac{19}{2}$

$\frac{49}{2}$

$\frac{29}{2}$

$\frac{39}{2}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & f(\mathrm{x})=\frac{5^{\mathrm{x}}}{5^{\mathrm{x}}+5} \\ & f(2-\mathrm{x})=\frac{5}{5^{\mathrm{x}}+5} \\ & f(\mathrm{x})+f(2-\mathrm{x})=1 \\ & \Rightarrow \quad f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+\ldots .+f\left(\frac{39}{20}\right) \\ & =\left(f\left(\frac{1}{20}\right)+f\left(\frac{39}{20}\right)\right)+\ldots .+\left(f\left(\frac{19}{20}\right)+f\left(\frac{21}{20}\right)+f\left(\frac{20}{20}\right)\right) \\ & =19+\frac{1}{2}=\frac{39}{2}\end{aligned}$

Question Tags

JEE Main

Mathematics

Medium

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