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在中学数学习题中,涉及n个数连乘积的题目屡见不鲜,中学生在解答这类问题时,普遍有困惑之感。本文通过五种方法的介绍,试图阐明这类问题的解题思路,对提高中学生的解题能力一定会有所裨益。方法1 直接相乘法计算n个数连乘积的一个方法是利用代数、三角公式,直接相乘。例1 计算3·5·17…(2~(2~(n-1))+1)(2~(2~n)+1) 解:原式=(2~2°-1)(2~2°+1)(2~(2~1)+1) (2~(2~2)+1)(2~(2~3)+1)…(2~(2~n)+1)
In high school mathematics problems, problems involving n number of consecutive products are common, and middle school students are generally confused when answering such questions. This article through the introduction of five methods, trying to clarify the problem-solving ideas of this type of problem, to improve the problem-solving ability of middle school students will certainly benefit. Method 1 Direct Multiplication One way to calculate the number of n products is to use algebra and trigonometric formulas to multiply directly. Example 1 Calculation of 3·5·17...(2~(2~(n-1))+1)(2~(2~n)+1) Solution: Original formula=(2~2°-1)(2 ~2°+1)(2~(2~1)+1) (2~(2~2)+1)(2~(2~3)+1)...(2~(2~n)+1 )