是个错题耶!1002应为1001.f(k)=4^k/(4^k+2)
f(1-k)=4^(1-k)/[4^(1-k)+2]
=4/(4+2*4^k).(分子分母同乘以4^k)
=2/(4^k+2)
所以,f(k)+f(1-k)=1
故f(1/1001）+f(2/1001)+.+f(1000/1001)
=[f(1/1001）+f(1000/1001)]+[(2/1001)+f(999/1001)]+...+f[(500/1001)+f(501/1001)]=1*500=500