if f(x) = 16^x/(16^x + 4)

Question

find f(1/2017) + f(2/2017) +f(3/2017) + ...+ f(2016/2017)

Answer 1

I have a sneaky suspicion that your function is

f(x) = 16^x/(16^(x+4) ) which would simply be
f(x) = 1/16^4 or 1/65536

in that case, f(4) = 1/65636 , f(13.56) = 1/65636 etc , doesn't matter what you have for the x value, since x does not show up in your function definition.

so f(1/2017) + f(2/2017) +f(3/2017) + ...+ f(2016/2017)
= 1/65636 + 1/65636 + 1/65636 + .... + 1/65636 , for 2016 terms
= 2016/65636
= 504/16409

If you meant it the way you typed it, we would have a rather cumbersome arithmetic problem.

Answer 2

should be:
f(1/2017) + f(2/2017) +f(3/2017) + ...+ f(2016/2017)
= 1/65636 + 2/65636 + 3/65636 + .... + 2016/65636 , for 2016 terms
= (1/65636)(1+2+3+...+2016)
= (1/65636)(1008)(1+2016) = 2033136/65636 = 508284/16409

Answer 3

the dangers of a simple typo, and the to copy-and-paste it ...

whenever you see 1/65636 it should say 1/65536>

so the final fraction is 2033136/65536 = 127071/4096