数列{an}中,a1=0,a2=3,a3=2,且an≥0,an+1·an=(an-1+2)(an-2+2)(n≥3,n∈N*）.试用数学归纳法证明：当

证：a3=2 a1+2=0+2=2 a3=a1+2,等式成立.假设当n=k(k∈N,且k≥3)时,等式成立,即ak=a(k-2)+2,则当n=k+1时,a(k+1)×ak=[a(k-1)+2][a(k-2)+2]=[a(k-1)+2]ak等式两边同除以aka(k+1)=a(k-1)+2=a[(k+1)-2]+2等式同样成立.综...