(1)∵数列{a[n]}满足条件：a[1]=1,a[2]=r,且数列{a[n]a[n+1]}是公比为q的等比数列
∴q≠0,r≠0,且a[n]a[n+1]=a[1]a[2]q^(n-1)=rq^(n-1)
∵a[n]a[n+1]+a[n+1]a[n+2]>a[n+2]a[n+3]
∴rq^(n-1)+rq^n>rq^(n+1)
1+q>q^2
即：q^2-q-1