A Study On The Methods Of Improving Students' Ability To Solve The Sequence Problems

As an important part of the content of high school mathematics curriculum,the sequence is the intersection of many mathematical knowledge.From the point of function,it is a special one,which is the category of discrete mathematics.During the learning of series,on the one hand,it can exercise students mathematical thinking and inspire students' mathematics thinking.On the other hand,it gives the foundation of higher mathematics to the learners.Therefore,in the secondary school,mastering the relevant content and methods of the series plays an important role for students to the further studying.The number of general formulas and the summation of the sequence are two cornerstones of the sequence content.They play core roles in high school mathematics and appear frequently in the calendar year.In addition,there are many types of problems diverse which need a strong skill and comprehensive,so it forces the students to have a high degree of logical thinking ability of thinking.In the college entrance examination,this part of the content mainly to the subject of moderate difficulty to examine,but since the new curriculum reforming,this part of the content of the test is to deepen the difficulty,which acquires the teachers more in the teaching of this content.The teaching plans and methods must be adjusted accordingly to ensure a better teaching effect in this challenge.On the basis of the research and analysis of the college entrance examination questions and questionnaire,combined with the author's own teaching practice,the following work is carried out.Firstly,the methods of how to solve the general formula of the sequence summarized were summarized:using the relationship between solving the general term formula,cumulative method,tired multiplication,to construct the auxiliary series method,trigonometric substitution,fixed point method,characteristic equation method and so on.Secondly,the summary of the common methods of how to sum the sequence was presented:universal analysis method,dislocation subtraction,group sum method,split phase compensation method,reverse order addition method;further for the college entrance examination focus on the difference between the sum of the series,Given other methods:formula method,derivative method,construction constant column method,Abelian method and so on.Thirdly,combining with the background of higher mathematics,a new method of serial number common formula was put forward under the high view of it.Finally,combined the learning and teaching practice,the three-level classification of the problem-solving method is carried out,and the teaching case of the summation of the difference ratio is designed,and a few suggestions of the teaching of the sequence were proposed,which gave an reference to the teachers.