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高职教材中有这样一个例题:已知无穷数列100/5,101/5,102/5,…,10n-1/5,…,求证:(1)这个数列是等比数列;(2)这个数列中任意一项是它后面第5项的1/10;(3)这个数列中任意两项之积仍然在这个数列中.教完这个例题后,很容易提出下面的问题,是否任意一个等比数列都具有性质:数列中的任二项之积仍是这个数列中的项?经过思考,大多数学生都能举出反例.如在等比数列{an}中,
There is such an example in the teaching materials of higher vocational colleges: we know infinite series 100/5, 101/5, 102/5, ..., 10n-1/5, ..., confirming: (1) This series is the geometric series; One after it is 1/10 of item 5 behind it, and (3) the product of any two of the numbers in this series is still in the sequence. After teaching this example, it is easy to ask the following question whether any one of the geometric series Has the nature of: the product of any two of the series is still the items in this series? After thinking, most students can give counterexamples, such as in the sequence {an}