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转换是最基本的数学方法,诸如将实际问题转换成数学问题,将这个数学分支问题转换成那个数学分支的问题等等.可以这么说:在全部的数学研究中,转换是无处不在的.灵活地、熟练地实现问题间的转换,是数学素养高的一个重要标志.下面例说几个常见的数学转换问题.一、等价问题的转换例1证明:不存在这样的正整数数列,它的项不都相等,而且从第二项开始,每一项都等于它的前一项和后一项的调和平均值(数2ab/(a+b)叫做数a、b的调和平均值).
Conversion is the most basic mathematical method, such as the conversion of practical problems into mathematical problems, the conversion of the mathematical branch into that mathematical branch, etc. It can be said that in all mathematics the conversion is ubiquitous. Flexible and proficient to achieve the conversion between problems is an important symbol of high mathematical literacy. The following example shows a few common mathematical conversion problems. First, the conversion of equivalence problems Example 1 proves: there is no such number of positive integer, Its terms are not all equal, and from the second term each equals the harmonic mean of its preceding and succeeding terms (the number 2ab / (a + b) is called the harmonic mean of a, b ).