Xueba starts with change

Chapter 206 Results
The latest page of the wrong title collection does record some wrong content.

But there are not many mistakes!

Compared with the previous one, Chen Zhou's calculation content was copied and pasted in large sections.

This time, the set of wrong questions only recorded a small part of Chen Zhou's mistakes in the research on the hail conjecture.

What is more critical is the time when the errors recorded in the wrong question set occurred.

It was all during the period when his thoughts were not smooth!

In other words, today is the last time for Chen Zhou to advance the progress of the project along the digital pyramid.

This also means that there is no problem with Chen Zhou's early thinking.

As long as the following research ideas are clarified, then this path is completely feasible!
How could this prevent Chen Zhou from falling into ecstasy?

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

Chen Zhou restrained his inner excitement a little bit, and carefully read the content recorded in the wrong question set.

The more this time, the more cautious we must be.

It is still possible to give up all previous efforts before reaching the final step and producing results.

"About the part of limm→∞Sm=1, didn't you consider it comprehensively?"

Chen Zhou frowned slightly, carefully recalling the thinking 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 wrong question set is that it points out all the mistakes.

But there is also a bad point, that is, it will not give the correct answer after pointing out the error.

This is very maddening.

Because all you can rely on is yourself.

You have to find out the cause of the error yourself, and then correct it so that it leads to the correct result.

However, Chen Zhou is already very satisfied that the wrong question set can have the current function.

If it is true that the wrong question set not only records the wrong content, but also gives the correct answer.

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

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

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

"has leaked!"

"If r=1→∞∑ar, 1=1 converges, and record its sum as S1, there will be, um... r=1→∞∑ar, 2=2S1-1..."

“同理，r=1→∞∑ar，3=3S1-2……”

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

Start debugging.

Chen Zhou's actions made the three of Zhao Qiqi look sideways.

I fell asleep on the bed, why did I get up again?
Looking again, Chen Zhou had already sat down at the desk with a pen and paper, and was writing furiously.

The three of them looked at each other unconsciously, all a little surprised, good guy, lying on the bed for a while, did you get inspiration?

Chen Zhou naturally didn't notice the expressions of the three brothers in the dormitory. All his attention is now on the white paper in front of him.

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

Chen Zhou, who was thinking like this, wrote a pen.

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

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

He didn't go back to bed again until around 2 o'clock in the evening.

In the dormitory at this time, the other three brothers had already fallen asleep.

Lying on the bed, Chen Zhou soon fell asleep too.

There was a smile on the corner of his mouth.

The ten hours of continuous work this time is finally no longer a waste of time.

The next morning, Chen Zhou woke up.

There is no way, I have something to do in my heart, and I can't sleep even if I want to sleep.

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

Chen Zhou was supposed to report to the museum today, but he has no other thoughts now.

While eating breakfast, Chen Zhou called Dean Yang.

He briefly expressed his request.

In this matter, Dean Yang said very straightforwardly that he will give you a fake approval, how long it will take, and you will fill it out yourself!
In this way, Chen Zhou temporarily put aside all matters other than Hail's conjecture.

Wholeheartedly buried in the hailstone conjecture.

Time always flies by at this time.

And Chen Zhou felt that there was not enough time.

He feels that the earth is running too fast these days.

From dawn to dusk, it was just a matter of him lowering his head and raising his head.

The fourth day after the military training.

library.

Chen Zhou and Yang Yiyi were still in their familiar positions.

Yang Yiyi is editing documents on the computer.

Chen Zhou is furiously writing.

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

In the past few days, all of Chen Zhou's time was spent on the research of the hail conjecture.

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

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

If not, turn over the wrong question set.

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

The one or two hours of thinking before turning over the wrong question set is also very good for error correction and verification of ideas after turning over the wrong question set.

This method is currently the most effective method that Chen Zhou feels.

As this period of time progresses, research on the hailstone 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 for a while, and began to prove it.

The tip of the pen touches the draft paper lightly, and the ink draws mathematical symbols on the paper.

Soon, the proof is over.

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

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, it needs to be proved that r=1→∞∑ar, 1 converges, and ≤1...]

After finishing writing, Chen Zhou did not pause at all, and began to prove this conclusion.

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

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

【...So, limr→∞∑r=1, rar, 1≤1...】

At this point, all the laying is complete.

There is only one last step left.

Chen Zhou took a deep breath and let it out slowly.

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

【……利用反证法，如果r=1→∞∑ar，1=S1＜1，那么S1-1＜0，进而就会有Sn=r=1→∞∑ar，n=n(S1-1)+1＜0，这里当n＞1/(1-S1)时成立。】

[This sentence is obviously wrong.Because they are all positive series. 】

[Therefore, r=1→∞∑ar, 1=1, established. 】

Chen Zhou's hands trembled slightly, so that the handwriting on the draft paper was slightly deformed.

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

[It can be deduced from this that the conclusion of the hail conjecture is correct.That is to say, all positive integers can become 1 through a finite number of hail conjecture operations. 】

……

(End of this chapter)