1. There are three ways to judge and prove that a sequence is arithmetic (proportional):
(1) Definition: Any natural number with n≥2 is verified as the same constant.
(2) General formula:
(1) if = +(n- 1)d= +(n-k)d, it is arithmetic progression;
(2) If it is a geometric series.
(3) The formula method of the middle term: verify that the formula of the middle term is established.
2. In arithmetic progression, the related maximum problem is usually solved by the adjacent term sign change method;
(1) When >: 0, d < When 0, the number of items m meets the maximum value.
(2) When
We should pay attention to the application of the transformation idea when solving the maximum problem of the sequence with absolute value.
3. The common methods of sequence summation: formula method, split item elimination method, dislocation subtraction, anti-addition, etc.
Third, matters needing attention in solving a series of problems
1. Prove that series is a common definition of arithmetic or geometric series, that is, by proving or obtaining.
2. When solving the problems related to arithmetic progression or geometric progression, the "basic quantity method" is a common method, but sometimes the flexible use of properties can make the operation simple, and the general sequence problem is often transformed into the solution of arithmetic progression and geometric progression.
3. The change of the relationship between attention and cognition. For example:
= , = .
4. The comprehensive problems of sequence limit have various forms and flexible solutions, but they are all inseparable from the concept, nature and mathematical thinking method of sequence limit. As long as we can grasp these two aspects, we can quickly get through the solution.
5. The success or failure of solving the comprehensive problem lies in examining the problem, understanding the context, grasping the essence of the problem through the representation of the given information, revealing the internal relations and implicit conditions of the problem, clarifying the direction of solving the problem, and forming the problem-solving strategy. Original link: /shuxue/shuxue/ Shi Zhi/288.html.