數列,數學歸納法,函數,不等式 f(x)=x-(3/2)x²,A1∈(0,1/2),A(n+1)=f(An),n∈N*,求證: An

數列,數學歸納法,函數,不等式 f(x)=x-(3/2)x²,A1∈(0,1/2),A(n+1)=f(An),n∈N*,求證: An

證明:函數f(x)=x-(3/2)x²=-3/2(x-1/3)²+1/6
它是(0,1/3)上為增函數,且函數f(x)<=1/6
1 當n=1時A1∈(0,1/2)
A1