Question

Let $f\left(x\right)=\frac{4^x}{4^x+2}$, then the value of $f\left(\frac{1}{1997}\right)+f\left(\frac{2}{1997}\right)+....+f\left(\frac{1996}{1997}\right)=$

• A. $998$
• B. $997.5$
• C. $998.5$
• D. $1996$

Answer 1

Answer: (A)

$998$

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

$f\left(x\right)+f(1-x)=1$

$f\left(\frac{1}{1997}\right)+f\left(\frac{1996}{1997}\right)=1,f\left(\frac{1}{1997}\right)+f\left(\frac{1995}{1997}\right)=1$

$\Rightarrow sum=\frac{1996}{2}=998$ and so on