The latest page of the set of errors does record some of the wrong content.

But there aren't many mistakes!

Compared with the previous one, a large number of paragraphs were copied and pasted from Chen Zhou's calculations.

This time, the set of errors only recorded a small number of errors in Chen Zhou's research on the hail conjecture.

What's more critical is the time when this part of the error recorded in the problem set is generated.

All during the time when his train of thought was not smooth!

That is, Chen Zhou is the last time to advance the progress of the project along the digital pyramid today.

This also means that Chen Zhou's early thinking is completely fine.

As long as the research ideas behind are clear, then this path is completely feasible!

How could this not cause Chen Zhou to fall into ecstasy?

After working for so long, I finally saw a glimmer of light before dawn!

Chen Zhou restrained the excitement in his heart a little, and carefully looked at the content recorded on the wrong question book.

The more this time, the more cautious it is to be.

Before the last step is reached, there is still a possibility that the previous efforts will be wasted.

"About limm→∞Sm=1, didn't you think about it comprehensively?"

Chen Zhou frowned slightly, carefully recalling the thought process of this part of the content in his mind.

This part of the content is the premise of the follow-up content, if you don't think about it comprehensively, it will definitely affect the follow-up content.

The only good thing about the problem set is that it points out all the mistakes.

But there is also a downside, that is, it does not give the right answer after pointing out the error.

It's maddening.

Because, you can still rely on yourself.

You have to figure out the cause of the mistake yourself and then correct it so that it leads to the right result.

However, the problem set can have the current function, and Chen Zhou is already very satisfied.

If it is true, the set of errors both records the wrong content and gives the correct answer.

Then he didn't dare to copy the answers directly and then publish the paper.

Because there is not a trace of his own thinking in this answer.

If published in a journal, how does he explain the key parts of it?

"Leaked!"

"If r=1→∞∑ar, 1=1 converges, and its sum is written as S1, there will be, huh...... r=1→∞∑ar，2=2S1-1......”

"Similarly, r=1→∞∑ar, 3=3S1-2......"

After Chen Zhou figured it out, he got up instantly and took out scratch paper and pen from his backpack.

Start correcting errors.

Chen Zhou's actions provoked Zhao Qiqi and the three of them to look sideways for a while.

I fell asleep in bed, why did I get up again?

Looking at it again, Chen Zhou was already sitting at the desk with paper and pen, and was writing hard.

The three of them looked at each other unconsciously, and they were all a little surprised, good guy, lie on the bed for a while, and then lie out of inspiration?

Chen Zhou naturally didn't notice the expressions of the three brothers in the dormitory, and all his attention was now on the blank piece of paper in front of him.

"The proof of this part of the content should be carried out by mathematical induction, from point to line, step by step to generalize to the general form......"

Chen Zhou, who thought like this, put pen to paper.

[Because ar,2=1/2(ar-1,3+ar,1)(r=1,2,3,...... , so that a0,3=0)......]

This night was the first time Chen Zhou stayed up late since cultivating good living habits.

It wasn't until around 2 p.m. that he went back to bed again.

At this time, in the dormitory, the other three brothers had already fallen asleep.

Lying on the bed, Chen Zhou soon fell asleep as well.

There was a hint of a smile on his lips.

This time, the work of more than ten hours in a row was finally no longer in vain.

Early the next morning, Chen Zhou woke up.

I can't help it, I have something in my heart, and I can't sleep if I want to.

It's better to hurry up and get this topic done.

Chen Zhou was supposed to report to the Courtyard today, but he didn't have any other thoughts now.

While it was time for breakfast, Chen Zhou called Dean Yang.

Briefly expressed his demands.

In this matter, Dean Yang said very happily, if you approve it, how long will it take, you fill it out yourself!

In this way, Chen Zhou temporarily put aside all the things other than the hail conjecture for the time being.

Single-mindedly buried in the hail conjecture.

Time flies by at this time.

And Chen Zhou felt that there was not enough time.

He felt that the earth was running too fast these days.

From dawn to dark, it was just a matter of him bowing his head and looking up.

On the fourth day after the end of military training.

Library.

Chen Zhou and Yang Yiyi are still in familiar old positions.

Yang Yiyi is editing documents on the computer.

Chen Zhou is working hard to write.

If you look closely, you can find that Chen Zhou's dark circles have appeared again, and the bags under his eyes have grown.

In the past few days, all of Chen Zhou's time has been spent on the study of the hail conjecture.

The correct way to open the wrong question set was also gradually mastered by Chen Zhou.

When his mind is not smooth, he will think for an hour or two to see if he can open his mind.

If not, then turn over the wrong question set.

Through the error guidance on the wrong question set, Chen Zhou first corrected the mistakes and then opened his mind.

The hour or two of thinking before turning the wrong problem set is also a good service for correcting errors and verifying ideas after turning the wrong problem set.

This method is currently the most effective method in Chen Zhou's opinion.

As this period progressed, the study of the hail conjecture.

Chen Zhou finally came to the last part.

【n=1→∞∑ar+1，n=n=1→∞∑ar，n-ar，1(r=1，2，3......) 】

Chen Zhou glanced at what he had written, thought about it for a while, and began to prove it.

The tip of the pen touches the scratch paper, and the ink traces mathematical symbols on the paper.

Soon, the proof was complete.

At the same time, according to the nature of series convergence, Chen Zhou also determined that "the convergence of n=1→∞∑a1,n ensures that all subsequent series converge", which is an important inference.

The pen in his hand paused slightly, Chen Zhou glanced at the proof process, and then wrote again:

[r=1→∞∑a1,n≤1, that is, r=1→∞∑ar,1 convergence, and ≤1......]

After writing, Chen Zhou did not pause in the slightest and began to prove this conclusion.

The proof of this conclusion is based on the previous proof process.

This conclusion can be proved by repeatedly applying the inference of the previous proof process.

【...... So, limr→∞∑r=1,rar,1≤1......]

At this point, all the foreshadowing is complete.

There is only one last step left.

Chen Zhou took a deep breath and then slowly exhaled.

After such a long period of research, it is finally time to produce results.

【...... Using the counter-argument method, if r=1→∞∑ar, 1=S1<1, then S1-1<0, then there will be Sn=r=1→∞∑ar, n=n(S1-1)+11/(1-S1) is true. 】

[This sentence is obviously wrong. Because it's all positive series. 】

[Therefore, r=1→∞∑ar, 1=1, is true.] 】

Chen Zhou's hands trembled slightly, so that the handwriting written on the scratch paper was a little distorted.

But in the end, Chen Zhou still wrote down that conclusion.

[From this, it can be inferred that the conclusion of the hail conjecture is correct.] That is, all positive integers can be calculated by a finite number of hail conjectures to become 1. 】

......