Volume 1: Student Life Chapter 206 Results
The latest page of the wrong question collection does record some incorrect content.
But there aren't many mistakes!
Compared with the previous one, large sections of Chen Zhou's calculation content were copied and pasted.
This time, the collection of wrong questions only recorded a small part of Chen Zhou’s mistakes in his research on hail conjecture.
What is more critical is the time when the errors recorded in the wrong question collection occurred.
All of this happened during the time when his thoughts were not flowing smoothly!
That is, Chen Zhou has the last time today to advance the progress of the project along the digital pyramid.
This also means that there is absolutely no problem with Chen Zhou’s early ideas.
As long as you sort out the subsequent research ideas , this path is completely feasible!
How could this not make Chen Zhou ecstatic?
After working so hard for so long, I finally see a ray of light before dawn!
Chen Zhou suppressed his inner excitement a little and carefully looked at the contents recorded in the wrong question collection.
Especially at this time, we should be more cautious.
Before reaching the final step and before the results come out, it is still possible that all the previous efforts will be wasted.
"Hasn't you considered the whole point about limm→∞Sm=1?"
Chen Zhou frowned slightly, carefully recalling his thinking process for this part in his mind.
This part of the content is the premise of the subsequent content. If it is not thought through comprehensively, it will definitely affect the subsequent content.
The only benefit of a wrong answer collection is that it points out all the mistakes.
But there is a downside, which is that after pointing out the error, it does not give the correct answer.
This is maddening.
Because the only one you can rely on is yourself.
You have to find out the cause of the error yourself and then correct it to the right result.
However, Chen Zhou is already very satisfied with the current functions of the wrong question collection.
If it is really a collection of wrong questions, it not only records the wrong contents but also gives the correct answers.
Then he didn't dare to just copy the answers and publish the paper.
Because there is not a single bit of his own thinking in this answer.
If published in a journal, how would he explain the key parts?
“It leaked!”
"If r = 1 → ∞∑ar, 1 = 1 converges, and we call its sum S1, we will have, um... r = 1 → ∞∑ar, 2 = 2S1-1..."
"Similarly, r=1→∞∑ar, 3=3S1-2..."
After Chen Zhou figured it out, he stood up immediately and took out draft paper and pen from his backpack.
Start error correction.
Chen Zhou's actions caused Zhao Qiqi and the other two to look at him sideways.
You had already fallen asleep on the bed, why are you getting up again?
When I looked again, Chen Zhou was already sitting at the desk with paper and pen, writing furiously.
The three of them looked at each other unconsciously, all a little surprised. Wow, just lying on the bed for a while, they got inspiration?
Chen Zhou naturally did not notice the expressions of the three brothers in the dormitory. All his attention was now on the piece of white paper in front of him.
"The proof of this part should be carried out by mathematical induction, from point to line, step by step to general form..."
Thinking of this, Chen Zhou started writing.
[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 developed good living habits.
He didn't go back to bed until about 2 a.m.
At this time in the dormitory, the other three brothers had already fallen asleep.
Lying on the bed, Chen Zhou soon fell asleep.
There was a hint of smile on his lips.
This time, working for more than ten hours in a row was finally not a waste of time.
The next morning, Chen Zhou woke up.
There's nothing I can do. I have something on my mind and I can't fall asleep even if I want to.
It is better to seize the time and finish this subject.
Chen Zhou was supposed to report to , but he had no other thoughts at the moment.
While having breakfast, Chen Zhou called Dean Yang.
I briefly expressed my demands.
In this matter, Dean Yang said very readily that he would approve the leave for you and it is up to you to fill in the length of time!
In this way, Chen Zhou temporarily put aside everything except the hail conjecture.
Immersed in the conjecture of hail.
Time always flies fast at this time.
Chen Zhou felt that there was not enough time.
He felt that the earth was moving too fast these days.
From dawn to dusk, it was just a matter of him lowering his head and raising it again.
The fourth day after the military training ended.
library.
Chen Zhou and Yang Yiyi were still in their familiar old positions.
Yang Yiyi is editing document materials on the computer.
Chen Zhou is writing furiously.
If you look closely, you can see that Chen Zhou's dark circles have reappeared and his eye bags have grown bigger.
These days, Chen Zhou spent all his time researching the hail hypothesis.
Chen Zhou gradually mastered the correct way to open the collection of wrong questions.
When his thoughts are stuck, he will think for an hour or two to see if he can open up his mind.
If that doesn’t work, then look through the collection of wrong questions.
Using the error guidance in the wrong question collection, Chen Zhou first corrected the mistakes and then opened up his mind.
The one or two hours of thinking before looking through the collection of wrong questions will also serve you well in correcting errors and verifying your ideas after looking through the collection of wrong questions.
Chen Zhou currently thinks this method is the most effective method.
As this period progressed, research on the hail hypothesis began.
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 took a look at what he had written, thought about it, and began to prove it.
The tip of the pen lightly touched the draft paper, and the ink outlined mathematical symbols on the paper.
Soon, the proof was completed.
At the same time, based on the convergence properties of the series, Chen Zhou also determined the important inference that "from n=1→∞∑a1, n converges, which guarantees that all subsequent series will converge."
The pen in his hand paused for a moment, Chen Zhou glanced at the proof process, and then wrote again:
【r=1→∞∑a1, n≤1, that is, we need to prove that r=1→∞∑ar, 1 converges and ≤1……】
After writing, Chen Zhou began to prove this conclusion without any pause.
The proof of this conclusion is based on the previous proof process.
By repeatedly applying the inferences of the previous proof process, this conclusion can be proved.
【……So, limr→∞∑r=1, rar, 1≤1……】
At this point, all the preparations are completed.
There is only one step left.
Chen Zhou took a deep breath and exhaled slowly.
After such a long period of research, the results have finally come.
[…Using the proof by contradiction, if r=1→∞∑ar, 1=S1＜1, then S1－1＜0, and then we have Sn=r=1→∞∑ar, n=n（S1－1）＋1＜0, which is true when n＞1/（1－S1）. ]
[This sentence is obviously wrong. Because they are all positive series. ]
【Therefore, r=1→∞∑ar, 1=1, holds. 】
Chen Zhou's hands were shaking slightly, so much so that the handwriting on the draft paper was somewhat deformed.
But in the end, Chen Zhou still wrote down that conclusion.
[From this we can infer that the conclusion of the hailstone conjecture is correct. That is, all positive integers can become 1 through a finite number of hailstone conjecture operations.]
…
