A function f(x) is given by f(x)=frac5^x5^x+5 , then the sum of the series f ((1)/(20) )+f ((2)/(20) )+f ((3)/(20) )+ldots+f ((39)/(20) ) is equal to :

Functions: A function f(x) is given by f(x)=frac5^x5^x+5 , then the sum of the… | JEE Main 2021

JEE Main 2021 (Online) 25th February Evening ShiftQuestion 1

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

Functions

$\frac{29}{2}$$\frac{49}{2}$$\frac{39}{2}$✓ Correct answer$\frac{19}{2}$

Solution

$f(x)+f(2-x)=\frac{5^x}{5^x+5}+\frac{5}{5+5^x}=1$. Pair $k$ with $40-k$: $19$ pairs give $19$, the middle term $f(1)=\frac12$. Sum $=\frac{39}2$.

Functions - JEE Mathematics question (JEE Main 2021 (Online) 25th February Evening Shift)

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