Question

if f(x)=4^x/4^x+2 find f(1/1999)+f(2/1999) +......+f(1998/1999)

Answer 1

notice that f(x)+f(1-x)=1.

hence f(1/1997)+f(1996/1997)=1,f(1/1997)+f(1995/1997)=1 and so on.

sum=(1996)/2=998