"I talked about Taylor yesterday, and the students have all understood, right? Understood? Didn't understand it? Did they understand it? Oh, some people have understood it, and some people are stupid and don't know. ”

This is Han Daxian's math class, he said: "Students who have not comprehended, I want to criticize you a few words, since you don't understand, why don't you come to me? I will answer your academic doubts for free, you apply for cram school outside, the tuition is not cheap, right? Be a man, the most important thing is to be happy." Learning, and most importantly, having fun. I can teach you math, but the fun course requires you to teach yourself. Students, are you happy?"

"Happy!"

"Unhappy ......"

Han Daxian stared at a boy: "Wang Yuhang, why are you unhappy?"

The boy was so embarrassed that he said, "Teacher Han, I'm Huang Yuhang......"

"I'm sorry, I remember, Wang Yuhang is in the second class, you two look very similar, even the hairstyle is exactly the same, both sides have a hairstyle with seven or three points on the top, like a brother. So Huang Yuhang, can you tell me why you're not happy?"

Huang Yuhang dared to appeal: "Teacher Han, mathematics is the king of science, I really want to learn mathematics well, but your teaching pace is too fast, I haven't fully comprehended the guidance, and you have already begun to talk about Taylor." ”

"I'm very depressed, a certain teacher complained that my teaching progress is conservative, but you say that my teaching pace is too fast, what is the standard? Why are you people's personalities so unstable? I don't even know how to go to class!" Han Da was angry, but also quite aggrieved.

"Teacher Han, your teaching rhythm is not fast or slow, the intensity is moderate, let's hurry into the teaching link. Li Zihan spoke up, and he said a fair word.

Han Daxian's mood was a little better, and he said with a pleasant face: "Li Zihan's recent progress is visible to the naked eye, and I am grateful. Li Zihan, are you happy?"

Li Zihan said beautifully: "I'm super happy!"

Han Daxian asked again, "Why are you happy?"

Li Zihan told truthfully: "I am very happy to be able to learn useful knowledge in Mr. Han's math class, hehehe." ”

Han Daxian nodded and said, "Excellent." ”

Next, entering the teaching session, Han Daxian said: "There is still some content of combinatorial identities that I have not finished, I will finish the combinatorial identities first, and then I will talk to you about calculus." ”

"Combinatorial counting and combinatorial identities are based on the permutation, combinatorial and binomial theorems of high school, their principles are simple, but the practical skills are very special, mainly to test the logical thinking, computing ability and flexibility of students. ”

"To be reasonable, combinatorial counts, combinatorial identities, and probabilities are self-contained and self-consistent, and are more difficult than entry-level calculus. Calculus is a tool to put it bluntly, so I'll put calculus at a later stage, do you think there's a problem?"

Han Daxian has a set of effective teaching plans, and the city's outstanding young teachers are not boasting.

"No problem!"

"Listen up!"

The students are enthusiastic, they can listen if they understand, and they are forced to listen if they don't understand.

（C0n）^2+（C1n）^2+（C2n）^2+…… （Cnn）^2=（2n）！/n！n！·

This equation is very representative, but it is difficult, time-consuming, and thankless to consider using basic combinatorial identities to prove this problem. Please note that the terms on the left are exactly the squares of the coefficients in the binomial expansion...... Li Zihan, will the mother function method be used?"

Han Daxian suddenly favored Li Zihan, and he named Li Zihan to answer the question.

As we all know, Lan Jie's mathematical strength ranks first in the class, and Li Zihan and Wu Zihan are tied for second.

Li Zihan's mathematics is quite strong, although he has not scored a perfect score in mathematics, he often scores more than 145 points.

Li Zihan, who was full of confidence, immediately gave an explanation: "(1+x)^n(1+1/x)^n is equal to 1/x^n, then the term containing x^n in (1+x)^2n is the n+1 term in the expansion, and the nth power of its binomial coefficient C2n is the constant term in (1+x)^n(1+1/x)^n, so it can be proved that (2n)!/n!n!·." That's what I know about the parent function method. ”

"The explanation is reasonable, the logic is clear, the thinking is flexible, and the cognition is profound. Han Daxian did not hesitate to praise him, he said: "Li Zihan, sit down, you have indeed improved, you are improving every day." ”

Li Zihan sat down happily, his performance was so good, he was deeply valued by Teacher Han, and won the love of his classmates.

Zihan knew that the girl in the middle of the third row must be paying attention to him.

It's a pity that Zihan, who is in the middle of the second row, has been transferred to the liberal arts class.

It would be great if Zihan was still in our second and third classes, and she could witness my Zihan's proud majesty with her own eyes.

Zihan was a little sad, he tried his best to prove himself in his studies, but he couldn't let his beloved Zihan see it.

Thankfully, there is also Yutong in the second and third classes.

"Using the binomial expansion as an auxiliary function, by comparing the coefficients of a certain term for calculation, this method is the parent function method, Li Zihan's explanation just now is basically correct, I will make some supplementary explanations......"

Han Daxian spent more than ten minutes explaining in detail the application of the parent function method in combinatorial identities, and he said: "There is a second solution to this problem, called the mathematical model method, with n blue balls and n red balls, and the number of ways to take out n balls from these 2n balls is Cn2n=(2n)!/n!(2n-n)!=(2n)!/n!n!·." ”

On the other hand, it can be regarded as n+1 ball fetching activity as follows: take r from n blue balls, and then (n-r) from n red balls, and the number of ways to take is CrnCn-rn=(Crn)^2, r is equal to 0, 1, 2, 3...... All the way to n, so the number of types of balls that match the topic is (2n)!/n!n!·. ”

"This method adopts the logical thinking method of 'counting twice', and verifies the answer by constructing a combined counting model of red and blue balls, and transforms abstract mathematical concepts into relatively concrete practical operations. ”

"Whenever you encounter this type of question, I strongly recommend the mathematical model method, the mathematical model method is practical, effective, easy to use, lottery players...... Oh no, the teachers and classmates have used it and said it's good. Class. ”

The bell rang for the end of class, and Han Daxian left quickly.

Click.

Lan Jie poked the back of Li Zihan's neck.

Li Zihan turned around suddenly: "What are you doing?"

Lan Jie said sincerely: "Brother Hanzi, you have become stronger again, and the mother function method you gave is exactly the same as I thought." ”

Li Zihan looked indifferent: "Oh, it turned out to be this matter, this is a trivial matter that is not worth mentioning." ”

Lan Jie continued: "The mathematical model method works, but in many cases, the parent function method and the mathematical induction method are more stable and more fault-tolerant, Zihan, what do you think?"

Li Zihan's body shook, and Lan Jie's words reached his heart.

"Lan Jie, are you okay, I'll go to the toilet if it's okay. ”

"Let's talk together, while walking. ”

"Going to the toilet is such a private thing, so you don't have to be together!"

Li Zihan went to the bathroom alone, and Lan Jie left the classroom half a minute later and came to the end of the corridor.

Ranger was about to enter the bathroom when he saw a man walking down the stairs.

The second (11th) class of high school is upstairs, and the person who came down is Su Zihan.

Su Zihan stopped, she smiled and waved her hand: "Hi, Lan Jie." ”

Seeing Su Zihan again after many days, Lan Jie missed it very much: "Su Zihan, you have lost a lot of weight, you have lost a lot of weight, and you have transferred to Class 11, is your pressure very great? Can you adapt to the rhythm of the liberal arts class? Are the new teachers and classmates good to you?"

Su Zihan touched her lower abdomen: "Are you kidding me? ”

"Su Zihan, your face is thin, it looks like you are thin, since your weight has not dropped, then I am relieved. ”

"Lan Jie, I've been studying your physics and chemistry homework for a long time, and I've always wanted to invite you to dinner, but I always haven't met a suitable opportunity, either I'm not available, or you have something. It's better to meet by chance, and make an appointment after school today?"

"Yes, by appointment. ”

"OK, see you after school. ”

Su Zihan continued to go downstairs, and Lan Jie entered the men's bathroom.