Liu Ze walked back to his seat, and the two children moved outside, still arguing, and when they heard what they discussed, it was really a freshman.

That girl is very beautiful, a bit like the milk tea sister, very elegant.

To be able to enter Jianghai University, it is the top of each high school, this is not before the start of school to come to the library to read, to become a top student must be diligent and hard-working, just from high school children love to learn.

The two argued a few more words, and the boy said excitedly: "This sequence A = (1+1/4) (1+1/9)(1+1/16)...... (1+1/n*n) is the multiplication of infinite terms, each of which is greater than 1, and it must not converge! ”

As she spoke, she drew an equation on the paper, and another girl said, "Not necessarily, I feel like I can converge!" "Girls sometimes just look at feelings.

"So how do you tell me how it converged? Convergence is necessarily bounded, and when it tends to infinity, even 1.000000001 is definitely infinite when multiplied together. ”

"Haven't you heard that even tissue paper can reach unimaginable heights when folded dozens of times in a row! This sequence has no boundaries at all! It is impossible to converge! The boy's words were very fierce, and there was no so-called pity and pity when arguing, and he couldn't say it when he questioned the girl like this.

The discussion was intense, and the voice was also very loud, it seemed that if you didn't help them solve this problem, don't think about being quiet, Liu Ze glanced at it casually and understood it in his heart, and said lightly: "This number series is indeed convergent!" ”

The boy glanced at him and said unconvinced, "How can you restrain yourself?" Can unbounded sequences converge too? ”

Liu Ze smiled, a very stubborn little boy, and asked rhetorically: "How do you know that this number series can't converge?" ”

"The first term of this sequence is 1.25, and the tenth term is 1.01, which must be infinite, supreme, and non-convergent!"

Seeing that Liu Ze supported his point of view, the girl was full of anticipation and said, "Classmate, do you know this question?" I think it will definitely converge, but I'm not going to prove it. ”

The topic of [Advanced Mathematics] is like this, once the thinking enters a dead end, it is difficult to make sense, Liu Ze is not in a hurry, and said with a smile: "I learned a formula in junior high school, remember, right?" As he spoke, he wrote on a piece of paper that (m-n) (m+n) is equal to the square difference between the two, which is a very common formula in junior high school.

The boy glared and said, "This formula is naturally known, and we are now discussing the topic of limit and convergence in [Advanced Mathematics], not junior high school pediatrics." That tone is quite proud, the high school entrance examination was the first in the city.

Liu Ze didn't say anything, and continued to write an equation on the paper, "It's a little difficult to prove the convergence of this number series directly, and it's easy to get into a misunderstanding, so it's better to change your thinking and take a detour to see that this number series B = (1-1/4) (1-1/9) (1-1/16)...... （1-1/n*n）！ ”

"Each term is greater than 0 and less than 1, so even if you multiply an infinite number of equations, the result must be greater than 0 and less than 1, right?" Liu Ze continued to guide the thinking of the two, which was an obvious result, and it was not difficult for them to understand.

"So what? This sequence is completely different from the one we talked about earlier! Because Liu Ze didn't agree with his point of view, the boy was a little mindful, and his words were very intense.

"Mathematics, if one road doesn't work, it's better to change the way and multiply the above two sequences, remember the equation I just said that I often used in junior high school?"

The paper reads A*B=(1-1/16)(1-1/81)(1-1/256)...... （1-1/n*n*n*n）。

"This newly generated number series is the same as the B number series just now, it must be greater than 0 and less than 1, bounded, convergent, can you understand it here?"

The two of them frowned and looked at it, and they both felt that such a change did have a great effect, but the key to it was still not understood, Liu Ze waited for a while and saw that the two of them had not seen it through, so they had to write another transformation on the paper, they were all top students, and the foundation was very good, so they suddenly realized.

Liu Ze wrote a more difficult number series and said: "In fact, the number series in this problem is not complex enough, and the results can be produced by simplifying it directly, and if it is a more difficult number series, it can reflect the value of this roundabout method!" ”

The boy looked at Liu Ze in surprise, his face was a little hot, it was true that he lost, but he was convinced, the person in front of him must have a deep accomplishment in [Advanced Mathematics], not only to speak clearly, but also to draw inferences.

The girl's face showed joy and said, "Wow, you must be a senior in the mathematics department, right?" It's so powerful, I've heard my cousin say that Jianghai University is full of cows, and that's really the case. ”

"No, I'm a master's student in the Institute of Electricity, you're only a freshman, and it's a bit of a detour to just start learning [Advanced Mathematics], the teacher talks quickly in class, and it's right to preview in advance."

The girl stood up straight, stretched out her hand, and said, "Hello senior, what a coincidence, we are also freshmen in the Electric Academy, my name is Yan Ling, this is my high school classmate Chen Cong, we are both Qidong Middle School in Jiangsu Province, high school is an experimental class, and we are still classmates." ”

It turned out that these two people came from Qidong High School in Suzhou Province, and Qidong High School almost knew among every student that they were very good at competitions and promotions, and the secret scrolls that flowed out of the school were circulated throughout the country.

Liu Ze stretched out his hand and shook Yan Ling Yan Ling loosened, Chen Cong stood there very unnaturally, Yan Ling touched him, the young man mustered up the courage to look up at Liu Ze, and also stretched out his hand and said, "Senior, I'm sorry, my tone just now was a little anxious, don't you mind." ”

Yan Ling also helped: "He's like this, haven't you heard that good men don't fight with women?" Every time you argue with me, it's like you're going to eat people, so ...... be careful."

"I ......" Chen Cong knew that he was indeed so.

Liu Ze shook his hand and said with a smile: "It's okay, academic discussions have always been like this, and sometimes there will be fights." ”

Yan Ling suddenly thought of something, and said excitedly: "Senior, let's move over and study with you, if you encounter a topic you don't understand, you can ask you nearby!" ”

Before Liu Ze could agree, the little girl ran in to clean up, and sure enough, she had the demeanor of an engineering girl, Chen Cong scratched her head embarrassedly, "I'll also go clean up and come with her, thank you, senior." ”

The two of them quickly moved out of it, and when they saw something they didn't understand, they could ask at any time, Liu Ze probably mentioned it, and the two of them could understand, but the frequency of their questions was not high, this is a typical scholar, when they see the knowledge points they don't understand, they must think about it by themselves first, read books repeatedly, do questions, and think, and then ask if they can't figure it out, so as to have a good effect.

Liu Ze was not too disturbed, he was bored, and took out the two mathematics [Matrix Theory] and [Numerical Calculation] that graduate students must learn, which are more obscure than the two courses of [Advanced Mathematics], and there are not as many reference books as [Advanced Mathematics], and there are even review guides for graduate school entrance examinations.

Liu Ze flipped through the two books quickly, drawing knowledge points, and directly wrote the writing steps when he turned to the after-class exercises, and suddenly thought of an idea, and quickly got up and went to the library to check the relevant technical literature, Yan Ling and Chen Cong were relieved to see him leave.

The two glanced at each other, Liu Ze was flipping through the book too fast just now, and he had been writing and drawing, studying with such a big cow, and the two freshmen also felt a lot of pressure, and looked at the [Matrix Theory] curiously, flipping through it.

Chen Cong grew his mouth and exclaimed: "Senior, these are two mathematics at the graduate level, I heard a neighbor brother of mine say that the mathematics course at the graduate level is very difficult, and I can't find a few reference books." ”

Yan Ling looked at [Numerical Calculation] and said: "The senior is really amazing, such a difficult [Advanced Mathematics] is the same as pediatrics in his eyes." ”

The girl's heart was full of admiration, and she thought to herself, if only she could study with her seniors every time.