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证明数列为等差或等比数列技巧

更新时间: 2020-11-05 00:00:00     

1、通常用定义法,等差数列:求证an-an-1为一个定值,则为等差数列。

2、等比数列:求证an/an-1为一个定值,则为等比数列.依题意,不妨设数列中连续3项为:a,aq,aq^2则:a-aq=aq-aq^2即:aq^2-2aq+a=0或:a*(q-1)^2=0所以只有:q=1

3、或者用中项法,等差数列:求证an+1+an-1=2an,等比数列:求证an+1*an-1=an平方

关键词: 证明 数列 等差 等比数列 技巧

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