F(X)=4^X\(4^X+2)求和式F(1\1001)+F(2\1002)+.........+F(1000\1001)的值

是个错题耶！1002应为1001.过程如下：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

500