The top student must be diligent.

Chapter 93 Method 3

Chapter 93 The Third Method

"It's the same rules as the last question. There are regular scores. Um... If you can solve this question, I guarantee you a minimum of 90 regular scores at the end of the semester."

While the students in the audience were thinking, Liu Bin continued.

He was naturally well aware of the difficulty of this question, so he offered a generous reward.

There will always be brave men when there is a big reward!
Then the next moment, a hand was raised.

Everyone was confused. This question looked extremely difficult. Who raised their hand so quickly?
They looked over and then all showed expressions of sudden enlightenment, it turned out to be God Xiao!

I almost forgot that Xiao Yi also came to class with them.

At this moment, Xiao Yi raised his hand with an eager look on his face.

The minimum score is usually 90.

Even though it wasn’t a perfect score, it was still worth it for him to raise his hand. Besides, it was his first class, so he should feel involved!

Of course, the most important thing is that this question suddenly gave him the inspiration to solve the possibility of the twin prime conjecture.

Maybe, if he were to try this question, it would bring some surprises?
However, after seeing Xiao Yi raise his hand, Liu Bin said with a smile: "Except you."

Xiao Yi's expression suddenly fell. Why?
"I've told you before that your grades have nothing to do with your performance in class, and you don't attend classes anyway."

defamation!

It's absolutely slander!
How can you defame someone's innocence out of thin air?

He defended himself: "I'm in class now!"

"I'm sorry, Xiao, the right to explain is mine."

Liu Bin spread his hands.

There was a burst of laughter in the classroom.

Xiao Yi widened his eyes. Wow, I never thought that Professor Liu is also a humorous person!
However, Liu Bin then changed the subject: "Of course, if you just want to do this question, then I welcome it, but I have a prerequisite."

"You have to solve this problem in at least two ways."

Xiao Yi's eyes twitched. How could he have class like this?
Students actively raise their hands to do the questions, but they still have to make conditions!

but……

Your hands are raised, so just do it!

Although it doesn't matter where you do it, he now sometimes has a metaphysical feeling that facing the vast blank space of the blackboard can stimulate some inspiration in his heart.

This is probably why top mathematicians still love blackboards and chalk?
However, he still said with a look of resentment: "Well, you are a professor after all!"

Liu Bin laughed and then said, "Then you can come up now."

Xiao Yi shook his head helplessly, then left his seat and walked to the blackboard.

The students below also stopped laughing and looked at their God Xiao with bated breath.

If they said that Xiao Yi had published in some awesome top journal, or had proved a conjecture that had long stumped the mathematics community, or had come up with some heavyweight theory, to them it was all just like castles in the air. They only knew that it was awesome, but they didn't know how awesome it was.

But at this moment, when they could see at a glance that this question was quite difficult and they had no idea how to solve it, Xiao Yi not only raised his hand immediately, but even faced with Professor Liu's condition of using two methods to solve the problem, he did not show any nervousness at all.

They can see this kind of awesomeness.

But, can Xiao Yi really come up with two methods?

……

“The first method.”

After getting on the podium, Xiao Yi started writing without any time to think.

"Considering this formula, we can easily see that it is actually equivalent to proving that—"

【lim(n→+∞)[nln(n)]/ln(an)=1】

As soon as this equivalent formula came out, the students below were immediately confused.

Is this what you mean by equivalent?

How did you get the equivalent? Only a few students showed an expression of sudden enlightenment after thinking for a while.

It turned out to be the case.

Liu Bin next to him also nodded with satisfaction. Although it was not unexpected, Xiao Yi's amazing observation skills always amazed him.

Of course, this problem cannot be easily solved after finding the equivalent relationship.

[First, pn>n, so lim(n→+∞)inf(lnpn)/lnn≥1]

【From the prime number theorem, we know that for l>1, lim(n→+∞)sup(pn)/n^l=0. 】

【From the arbitrariness of l>1, we know that...】

【Finally, according to Stolz's theorem, we can get: lim(n→+∞)……=1】

【The proof is complete.】

After seeing this prime number theorem and then adding the Stolz theorem used in the previous question, more than half of the students immediately surrendered.

I can’t do it. I really can’t do it.

If they hadn't looked at Xiao Yi's method, they would never have thought of how to use these two theorems successively.

Especially the prime number theorem, which is also included in the content of high school mathematics competitions. For the students in Hua Luogeng's class, they basically know this theorem. When they saw Xiao Yi use it, they felt as if they had suddenly been enlightened.

This is God Xiao!
“Here’s the second method.”

After solving the problem with the first method, Xiao Yi started writing the second method on a new line.

If the first method is a clever method, then the second method is hard evidence.

Just like the hard-evidence method that Ye Cheng used in the previous question.

Obviously, this method looks more "showy".

With the 29 classmates in the class staring in amazement, Xiao Yi used almost every method they had learned in mathematical analysis to the limit and finally completed the proof of this problem.

"it is good!"

Ye Cheng, who was below, immediately stood up and clapped his hands vigorously, "As expected of my Brother Xiao!"

The other students also reacted and applauded.

"God Xiao is awesome!"

Liu Bin, who was standing on the side of the podium, also smiled and clapped his hands. He walked up to the stage and said to Xiao Yi, "Very good, very good. It seems that this kind of question is nothing to you."

Xiao Yi waved his hand modestly and said, "You just haven't made the questions more difficult yet."

Liu Bin curled his lips and said, "If this isn't difficult enough, how much more difficult do you want it to be?"

Waving his hand, he said, "Okay, you can go back to your seat."

However, at this moment, Xiao Yi said: "Professor, please wait a moment, I have another method that I would like to try."

"There's another way?" Liu Bin was stunned, then nodded: "Then you try it."

The students below were also slightly stunned.

Two methods are not enough for you?
Or even want to use a third method?

Ye Cheng: "Stand back, my brother Xiao is going to start showing off!"

……

Xiao Yi stood on the other side of the blackboard, thinking about the screening method that had been circling in his mind for a long time.

Ok……

I still have no idea for now, but let's use the sieve method to solve this problem first.