论文部分内容阅读
2011年高中数学联赛湖北省预赛中有如下试题:已知数列{a_n}满足a_1=1/3,a_(n+1)=a_n+a_n~2/n~2(n∈N~*).证明:对一切n∈N~*,有(1)a_b1/2-1/(4n).标答给出的证明非常巧妙,尤其是第(2)小问,需要构造递推不等式,成功完成此题需具备较强的代数变形能力和放缩技巧.笔者通过研究,发
In 2011, the high school mathematics league in Hubei province preliminaries have the following questions: The known sequence {a_n} satisfies a_1 = 1/3, a_ (n + 1) = a_n + a_n ~ 2 / n ~ 2 (n∈N ~ *). Proof: For all n∈N ~ *, there are (1) a_b 1 / 2-1 / (4n) Is the second (2) small question, need to construct recursive inequality, the successful completion of this subject need to have a strong algebraic deformation ability and scaling skills.The author through research, hair