(1)(a3)^2=a2*a4,2a4=a3+a5
解得a3=3/2,进而a1=2*a2-a3=1/2
(2)根据需要证明的结论猜想a(n+1)/an递减
即a(n+2)/a(n+1)-a(n+1)/an≤0恒成立,化简为an*a(n+2)-a(n+1)^2≤0
当n=2k(k∈N+)时
an*a(n+2)-a(n+1)^2=0成立
当n=2k+1(k∈N+)时
an*a(n+2)-a(n+1)^2=-(an-a(n+2))^2/4≤0成立
然后需要证明a3/a2-a2/a1<0
(a3*a1-(a2)^2)/(a1*a2)=-(a2-a1)^2/(a1*a2)<0
故当n≥2时a(n+1)/an<a2/a1