我们知道 ,由数列极限定义知 :当limn→∞an存在时 ,limn→∞an+1 =limn→∞an.那么这个结论在解题中有什么应用呢 ?例 1　已知limn→∞an 存在 ,且limn→∞2anan+1 + 1 =1 ,求limn→∞an 的值 .分析　设limn→∞an =A .∵　limn→∞2anan+1 + 1 =1 ,∴　2limn→∞anlimn→∞an We know that we know by the definition of series limit: when limn → ∞an exists, limn → ∞an+1 = limn → ∞an. Then what is the application of this conclusion in the solution? Example 1 It is known that limn → ∞an exists , and limn → ∞ 2anan +1 + 1 =1, find the value of limn → ∞an. Analysis set limn → ∞an = A. ∵ limn → ∞ 2anan +1 + 1 =1, ∴ 2limn → ∞anlimn → ∞an