论文部分内容阅读
在根式运算过程中,为了计算简捷,常常需要将分母有理化,因此分母有理化作为根式运算的重要内容在教学过程中已得到一定的重视。但提起分子有理化,大部分学生对此都感到比较生疏,甚至认为是多此一举。在教学过程中,部分教师对分子有理化这一内容亦存在着偏见,对它没有引起应有的注意。其实,分子有理化在解题中的某些特殊作用,有时并不亚于分母有理化。请看下列几例: 例1 求证1+1/(2~(1/2))+1/(3~(1/2))+…+1/(n~(1/2))>2((n+1)~(1/2)-1)(n为自然数)
In the process of root-based computing, the denominator often needs to be rationalized for the sake of simple calculation. Therefore, the rationalization of the denominator, as an important part of the root-based operation, has gained some attention in the teaching process. However, the reason for the rationalization of the molecule is that most students feel unfamiliar with this, and even think that it is an extra one. In the teaching process, some teachers also have a prejudice against the content of the rationalization of the molecule and have not paid due attention to it. In fact, some of the special effects of the rationalization of molecules in problem solving are sometimes not inferior to the rationalization of denominators. Please see the following examples: Example 1 Verify 1+1/(2~(1/2))+1/(3~(1/2))+...+1/(n~(1/2))>2 ((n+1)~(1/2)-1) (n is a natural number)