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51问答网 > 怎么证明斯托尔茨定理？高等数学

怎么证明斯托尔茨定理？高等数学

2025-03-15 10:04:47

推荐回答（1个）

回答1：

证明思路：
设l=lim[(An-An_1)/(Bn-Bn_1)]，对任意e>0，根据极限定义，那么从某项N开始，
l-e<(An-An_1)/(Bn-Bn_1)然后因为Bn递增，三项同乘Bn-Bn_1，再从N到n求和，就得到类似
(l-e)(Bn-BN)最后加上AN再同除Bn即可。

l-e<(An-An_1)/(Bn-Bn_1)三项同乘Bn-Bn_1

再从N到n求和啊

l-e<(An-An_1)/(Bn-Bn_1)（l-e）(Bn-Bn_1)<(An-An_1)<（l+e）(Bn-Bn_1)
（l-e）(Bn_1-Bn_2)<(An_1-An_2)<（l+e）(Bn_1-Bn_2)
……………………

（l-e）(BN_1-BN)<(An_1-AN)<（l+e）(BN_1-BN)

把上面N个式子相加后，中间的项都抵消了，结果就是

(l-e)(Bn-BN)

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