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数列是初等数学重要的内容之一,也是“学数学、用数学”的重要载体之一,它能有效培养与检测学生的创新能力和数学素养。整体思想,就是从全局着眼,由整体入手,把一些表面上独立而实质上紧密联系的量作为整体考虑的思想方法。应用整体思想解决数列问题,能很快抓住问题的本质,体现思维的敏锐性、独创性、深刻性,同时可以优化运算过程,节省解题时间,快速而准确地解决问题。下面举例介绍整体思想在解决数列问题中的应用。
The sequence is one of the important contents of elementary mathematics. It is also one of the important carriers of “mathematics and mathematics”. It can effectively cultivate and test students’ innovative abilities and mathematical literacy. The whole idea is to think globally and start from the whole. Think of a number of seemingly independent but closely connected entities as a whole. Applying the whole idea to solve a series of problems can quickly grasp the essence of the problem, reflect the sensitivity, originality and profoundness of thinking. At the same time, it can optimize the calculation process, save solution time and solve problems quickly and accurately. The following examples illustrate the application of the whole idea in solving the sequence of problems.