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证明数列为等差或等比数列技巧

更新时间： 2021-02-03 00:25:18

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

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