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高二代数課本数列这一章的习題里,有几个題目是分別带有1,2,3,…,n,…个(或0,1,2,3,…,n,…个)循环节而构成的数列問題,同学作題时,常因不知这些数列的通項公式而感到困难。虽經教师指导,但仍不明白道理。因此。将这类問題提出来和大家討論。研究这样的数列的通項公式,让我們先来研究下面的例題。例1.求数列:0.3,0.3,0.333,……的通項。 [解] 我們从第2項起,每一项真减去它前边的一項,連同原数列的第一項,便得一个新数列: 0.3,0.03,0.003,……。显然,这个数列是一个无穷递缩等比数列,它的首項就是原数列的首項(0.3),公比是1/10,因此它的前
In the exercises of this chapter of the second-generation algebra textbook series, there are several topics with 1,2,3,...,n,... (or 0,1,2,3,...,n,...) cycles. The problem of the series formed by the festival, when classmates make questions, they often find it difficult to know the general formula of these series. Although teachers have given guidance, they still do not understand the truth. therefore. Ask these questions to discuss with you. To study the general formula of such a series, let us first study the following examples. Example 1. Finding the number column: 0.3, 0.3, 0.333,... [Solutions] From the second item, we subtract each item from its front one, and together with the first item of the original number, we get a new series: 0.3, 0.03, 0.003, .... Obviously, this sequence is an infinitely-reducing geometric series whose first term is the first term (0.3) of the original sequence, and the common ratio is 1/10, so its former