Question bank/JEE Advanced/Mathematics

Let the function $f:[0,1] \rightarrow \mathbb{R}$ be defined by

$$f(x)=\frac{4^{x}}{4^{x}+2}$$

Then what is the value of
$$f\left(\frac{1}{40}\right)+f\left(\frac{2}{40}\right)+f\left(\frac{3}{40}\right)+\cdots+f\left(\frac{39}{40}\right)-f\left(\frac{1}{2}\right)$$?

Source: JEEBench (IIT Delhi) / JEE Adv 2020 Paper 2