众所周知,线性递推式问题已经有了较为成熟的求解方法,如待定系数法、特征根法、不动点法、母函数法、矩阵法等.而非线性递推式的求解则是一个难点,这类递推式往往结构复杂,没有固定的模式可套,方法多姿多彩,因此一直是各类竞赛的热点和难点问题.其中,含根式的非线性递推式在近几年的竞 As we all know, the linear recursive problem has been more mature solution, such as undetermined coefficient method, eigenvalue method, fixed point method, the mother function method, the matrix method, etc. Nonlinear recursive solution is a difficult , These types of recursive models are often complicated in structure and have no fixed model, so they have been hot and difficult issues of all kinds of competitions. Among them, the non-linear recurrence with roots is competitive in recent years