因为a(n+1)≥an≥a1
所以an>0
[a(n+1)+an-1]²=4a(n+1)an
那么[a(n+1)]²+2a(n+1)an+an²-2a(n+1)-2an+1=4a(n+1)an
[a(n+1)]²-2a(n+1)an+an²-2a(n+1)+2an+1=4an
[a(n+1)-an]²-2[a(n+1)-an]+1=4an
[a(n+1)-an-1]²=4an
a(n+1)-an-1=2√an 或 1+an-a(n+1)=2√an
如果a(n+1)-an-1=2√an
a(n+1)=an+2√an+1=(√an+1)²
√a(n+1)=√an+1
所以{bn}是以1为首项,1为公差的等差数列
如果 1+an-a(n+1)=2√an
(√an-1)²=a(n+1)
√an-1=√a(n+1)
所以{bn}是以1为首项,-1为公差的等差数列
综上,{bn}是等差数列