1.Relation and Function
medium

एक फलन $f ( x ), f ( x )=\frac{5^{ x }}{5^{ x }+5}$, द्वारा दिया गया है, तो श्रेणी $f \left(\frac{1}{20}\right)+ f \left(\frac{2}{20}\right)+ f \left(\frac{3}{20}\right)+\ldots \ldots+ f \left(\frac{39}{20}\right)$ का योगफल बराबर है

A

$\frac{19}{2}$

B

$\frac{49}{2}$

C

$\frac{29}{2}$

D

$\frac{39}{2}$

(JEE MAIN-2021)

Solution

$f(x)=\frac{5^{x}}{5^{x}+5} \quad f(2-x)=\frac{5}{5^{x}+5}$

$f(x)+f(2-x)=1$

$\Rightarrow f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+\ldots+f\left(\frac{39}{20}\right)$

$=\left(f\left(\frac{1}{20}\right)+f\left(\frac{39}{20}\right)\right)+\ldots+\left(f\left(\frac{19}{20}\right)+f\left(\frac{21}{20}\right)+f\left(\frac{20}{20}\right)\right)$

$=19+\frac{1}{2}=\frac{39}{2}$

Standard 12
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.