拉马努金等式的证明及推广

The Proof and Generalization of Ramanujan's Equation

对于拉马努金等式,本文首先应用数列极限的方法给出其收敛性的证明.再结合式中多重根号嵌套的结构,通过构造函数方程,给出一个推广的结果.并将这种方法推广到一般形式,最后得到了此类极限的收敛性的一般判别法.文中使用的方法,为无穷根号形式的极限问题提供了系统化思路,丰富了极限的表达形式.

For the Ramanujan＇s Equation,we give the proof of convergency by sequence limit firstly.Then construct a function equation for the square roots,and show a wider conclusion.In the end,we generalize the method to the general situation,and give a criterion for this kind of limit.The discuss in this article give a unitive train of thought of infinite square roots,and supplement the expressions of limit.