If f(x) = 4^x(4^x+2)^-1 for all x belongs to R , then f(1/1997)+f(2/1997)+.........+f(1996/1997) =

Options are 197.5,998,1998,999

f(x)= 4^x(4^x+2)^-1       and f(1-x)= 2(4^x+2)^-1

f(1996/1997)= f(1-1/1997) and similarly next all

now, f(x) + f(1-x) = 1

f(1/1997)+f(2/1997).........+f(1-2/1997)+f(1-1/1997)

making pairs...

total pairs=1996/2=998

so, sum=1+1+1+1+..998 times=998

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