How to learn the number series is easy to learn, I think the number series is so difficult, how to l

Work your ability to find patterns. (Exercise eyesight, answer in seconds at a glance) be familiar with the commonly used number series, and be familiar with the way of "number series set of number series".

For example. a(n)=2 n you are familiar with.

Can you write a recursive formula?

a(n+1)=2a(n)

a(n)=2 n+nCan you write a recursive formula?

a(n+1)=2*2 n+n+1=2a(n)+1-n, so if I give you a recursive formula that is: a(n+1)=2a(n)+1-n, can you write a(n)?

a(n)=2 n+n 2Can you write a recursive formula?

So if I give you the recursive formula, can you write a(n)?

a(n)=n*2 n+1Can you write a recursive formula?

So if I give you the recursive formula, can you write a(n)?

Familiar with commonly used methods, eigenroot methods, fixed point methods, etc. You don't need to understand the deceptive tricks of Shenma superposition.

Any sequence of numbers you can come across on the exam is constructed from a series of proportional and differential numbers.

a(n)=n is a series of equal differences.

a(n)=n 2 is "the difference is the difference series", that is, b(n)=a(n)-a(n-1) is the difference series.

Find a certain pattern, find the type of problem to solve, but first you must know those formula concepts.

The knowledge of number series in high school is not very difficult, if you find it difficult, it is recommended that you do the exercises in the textbook several times, and you must master the basic definition formula.

1. To learn the number series, you must first master some basic formula points. For example: find the general term, find the sum of the first n terms;

2. You should remember the basic sequence formula, after all, the formula is like a brick for building a wall, you can't build a wall without bricks, on this basis, take a look at the example problems, the example problems must be representative;

3. Familiarize yourself with the formula by learning more and doing more;

4. Understand the question types of number series, such as: abstract number series question types, combined with functions;

5. After that, try to do simple questions;

6. Slowly increase the difficulty, so that it will be easier to master and learn to solve the number series.

To learn the number sequence, you first need to know some basic publicity. To find the general term, find the sum of the first n terms, several formulas are definitely required, such as s(n+1)-sn=an This is the most basic way to find the general term.

Mathematics is about learning more and doing more. The formula is not for memorization, it is cooked...

The question type of the number series in the college entrance examination is not difficult, it is nothing more than finding the middle term of an, sn and other ratios and the middle term of equal difference are often used.

Here's my personal opinion. There are three levels of the number series in high school.

1) Basic question types. You need to summarize this yourself, such as multiplication and common ratio, dislocation subtraction, list method, and so on. These things feel difficult to learn at first, and you will definitely not be used to them, so you need to summarize the question types and then practice according to the question types.

After a while, you will be able to get full marks for this section.

2) Think about the question type. This section often has some regular questions for you to find out the general formula, or to overturn it. The specific methods are ever-changing, and there is no good response to it, only one can be encountered and one can be killed.

3) Puzzles, don't think about this part, use to put things that these universities won't ask for... The college entrance examination is generally the last finale question. . . And it's the level of the third question.,Let's not want it.,Just take the test 144.。。。

In order to get a high score, you have to focus on part (1). Part (2) After passing part (1), do the questions appropriately. Part (3) suggests abandonment, which makes no sense.

Hello, if it is college entrance examination mathematics, the general term and sum of the difference and proportion of the two basic sequences in the number series must be mastered, and the method of finding the second-order linear recursive sequence can be taught by yourself. If it is a competition mathematics, it is more demanding, and the various methods of finding the second-order linear recursive number series need to be mastered, and there may be knowledge of number theory in it.

In addition, it is always beneficial to do more questions and summarize the experience.

It can be seen that then I suggest you read some of the basic methods given to you by the teacher, such as the ......... of eliminationI think your teachers have told you, as for what you said above, you can't do it when it comes to exams, I have had this experience before, it may be that the foundation is not good, or it may be that you blindly pursue some more difficult methods, and ignore some of the usual basic methods.

It's a bit difficult, but it's good to memorize the fixed formula of the book first, and then practice and consolidate it more.

People think that the number series is difficult to learn because they didn't listen carefully to the lectures from the beginning, so that they will find it difficult later.

Summary. Hello dear, the content of the information you queried is: To learn the number series well, you must first have a deep understanding of the concept, what is the former item, and the latter item.

What is the nth term, the difference between the number series an plus not the parentheses. the definition of a series of equal differences, and so on. Be clear about the ** of each formula.

There will be a lot of formulas in the number series part, and when you first learn, you must understand the derivation process of the formula, and clearly understand the formula** in order to apply it flexibly. At the same time, it is necessary to know the methods that are often referred to as accumulation, accumulation and multiplication construction.

Hello dear, the content of the information you queried is: To learn the number series well, you must first have a deep understanding of the concept, what is the former item, and the latter item. What is the nth term, the difference between the number series an plus not the parentheses.

the definition of a series of equal differences, and so on. Be clear about the ** of each formula. There will be a lot of formulas in the number series part, and when you first learn, you must understand the derivation process of the formula, and clearly understand the formula** in order to apply it flexibly.

At the same time, it is necessary to know the methods that are often referred to as accumulation, accumulation and multiplication construction.

The number series pays attention to the problem of finding the general term, the problem of reducing the difference to the ratio of the number series and the summing problem, and the rest is nothing. Pay attention to the summary method, multiplication and dislocation subtraction, accumulation and multiplication, etc.!

When and how to use the cumulative multiplication, split term elimination method and dislocation subtraction method.

The cumulative multiplication formula is an = 2n (n+1), which is a method specially designed to solve the general term formula of the series, a series of numbers arranged in a certain order is called a series, and the nth term of the series is expressed by a specific formula, which is called the general term formula of the series. Split-term expression: 1 [n(n+1)]=1 n)-[1 (n+1)] dislocation subtraction It is suitable for summing the first n terms of a type series, where is an equal difference series, and is an equal proportional series.

1. The thinking method of functions.

The sequence itself is a special function, and it is a discrete function, so in the process of solving the problem, especially when encountering the two special types of sequences of equal difference and proportional series, they can be regarded as a function, and then the properties and characteristics of the function can be used to solve the problem.

2. The thinking method of equations.

This chapter involves a number of mathematical formulas about the first term, the last term, the number of terms, tolerances, tolerances, tolerances, the nth term and the first n terms and these quantities, and the formula itself is an equation, so in the process of finding these mathematical quantities, they can be regarded as the corresponding known quantities and unknowns, and the equations about finding unknown quantities can be established through formulas, which can make the solution clear and clear, and simplify the process of solving the problem.

3. Incomplete induction.

The incomplete induction method can not only cultivate students' mathematical intuition, but also help students solve problems effectively.

4. Reverse order addition.

In the process of deriving the first n terms and formulas of the equal difference series, the reverse order addition method is well applied according to the characteristics of the equal difference series, and this method is directly or indirectly used in many problems in this chapter.

5. Dislocation subtraction.

Dislocation subtraction is another type of method for summing sequences, which is mainly applied to the summation of terms that can be converted into each other through a certain deformation, and is a problem of summing multiple numbers. This method of thinking is used in the derivation of the first n terms and formulas of proportional sequences.

Sequences and inequalities should be easier to learn.

The main series should pay attention to the problem of finding the general term, the problem of reducing the difference to the proportional series and the problem of summing, and the rest will be nothing.

Pay attention to the summary method, multiplication and dislocation subtraction, accumulation and multiplication, etc.!

Inequalities: Remember important inequalities.

The square mean is greater than or equal to the arithmetic mean, the geometric mean is greater than or equal to the harmonic mean, etc., and it is good to find relationships and skills!

The most important topic in the study of number series is to discuss the limits of number series, which will be studied in more depth in higher mathematics. In higher mathematics, series (i.e., the sum of sequences) are also studied in depth.

In middle school, in addition to learning some of the most basic concepts in the number series, I thought that as long as I learned the equal difference series and the proportional number series, I would be fine.

1. Proficient in the concepts of equal difference series and proportional series, including definition, tolerance and proportion, etc.;

2. Be able to write the general formulas of the equal difference series and the equal proportion series, know the properties of the equal difference and the proportional middle term, and use these properties;

3. Write the sum of the first n terms of the equal difference series and the proportional series.

If you have figured out the above concepts, you will learn the number sequence part.

It should be pointed out that it is very difficult, even impossible, to write the general formula of the number series and the sum of the first n terms for the general number series, and there is no need to spend too much energy and time in this regard, because no matter how much energy is used, it may not be able to achieve any results. I often see this kind of problem here, that is, you write a few numbers and ask what number appears in the middle or behind, which is actually a game, not math, and it is not good for learning math.

The number series mainly examines the ability to observe and induct. There are many ways to prove it, and it is more flexible, and if you are not very good at mathematics, it is impossible to learn the number series alone. If you don't know how to do it at the beginning, then when looking at the example problems, don't think that you are done after reading it, and do it yourself, and even try other methods, for example, most of the number series can be proved by induction, and some of the related sequences can be turned into a(n+1)+kan = m(an + ka(n-1)), so that a(n+1)+kan is an equal ratio series.

Of course, there are many methods, and if you don't learn well, you should practice more and try more new methods and old methods.

Read the book first and fully understand the book.

Understand how the formula of the number series came to be, and then memorize it to death.

In high school mathematics, the study guidance of the number series is suggested:

1. Understand the original meaning of the number series: a set of ordered numbers, a row of numbers; Among them, "regular sequences" are the main research objects.

2. The key is to grasp the meaning of an and sn and the relationship between the two (implied condition), and find the expression f(n) of the two from the given known relationship (additional condition).

To do the second point (the second point is also the most practical point, the study of the number series is to require an and sn)].

3. Familiar with and master the conclusions, solution methods, and derivative sequences of the two typical sequences of [Proportional Series, Equal Difference Series] (such as the method of finding a series of "an=equal difference series bn·equal proportional series CN").

4. Use the above solution methods as a "big shield" to challenge your goals (high school mainly refers to college entrance examination questions).

Sort out the logic of each step in the actual combat (thinking before each big step, why do you ask for this next?). Why use this method? ）；

When doing questions in actual combat, keep looking for which ones can be used in the "big shield", and try it;

If there is a new method, on the one hand, you should think about "whether it is really new and whether it is caused by some special conditions", and on the other hand, create a new notebook to write it down (but you don't need to summarize it like "Big Shield", if these new situations are recorded to a certain number, it means that you need to study them and summarize them; Otherwise, it only needs to be treated as a "special case" and as an "experience", and there is no need to pursue 100% perfection).

To sum up, combined with the learning process of "theory, actual combat, and experience", the important thing is "how much can be used in actual combat", and learning a good number series has little to do with personal IQ: learning psychology tells us that any skill can be learned through enough exercise!!

Focus on mastering the method and properties of the equal difference series and the proportional number series, learn how to find the general term formula an and the first n term and sn, master the common methods of finding the general term formula (definition method, construction method, conjecture and mathematical induction method, etc.), and master the method of finding sn (there are mainly several methods: definition method (equal difference series and equal proportion series), superposition method, dislocation subtraction method (a difference series multiplied by a proportional number series), group summation method (generally a proportional number series plus an equal difference number series), Split term elimination method (e.g., 1 (1*2)+1 (2*3)+...1/n(n+)=1-1/2+1/2-1/3+……1 n-1 (n+1)=1-1 (n+1)=n (n+1) is actually a formula:

1 n(n+1)=1 n-1 (n+1) is the split), apply the formula (if an=n 2 is known to find sn, you can use the formula: 1 2+2 2+3 2+......).n 2=n(n+1)(2n+1) This can only be done by memorizing the common formula) In addition, there are some other methods, and it is up to you to keep summarizing them in actual combat! Finally, it's essential to do a lot of practice!

Good luck with your studies!