已知数列｛an｝满足a1=3,a(n+1)=an^2-nan+λ（n∈N*,λ为实数）
问题描述：
已知数列｛an｝满足a1=3,a(n+1)=an^2-nan+λ（n∈N*,λ为实数）
(1）若an≥2n恒成立,求λ的取值范围
（2）若λ=-2,求证1/(a1-2)+1/(a2-2)+……+1/(an-2)＜2
答
(1)a2=a1^2-a1+λ =6+λ>=4 λ>=-2a3=a2^2-2a2+λ=(6+λ)^2-2(6+λ)+λ=36+12λ+λ^2-12-2λ+λ=λ^2+11λ+24>=6λ^2+11λ+18>=0 (λ+2)(λ+9)>=0 得λ>=-2 或λ=2 得a(n+1)/(n+1) =(an^2-nan+λ)/(n+1)>=2an^2-nan+...