Xueba, I beg you to go and escort him quickly!

It can be seen from the mathematical induction method that the formula ② holds for all positive integers n, so the proposition is proved.

Done!

The whole place went quiet.

Xu Heng looked left and right, "What's your opinion?"

No wow!

If someone else writes a question, you can start discussing it within a few seconds!

Why don't you say anything when I ask this question?

"Wait a minute! Let's digest your problem-solving thinking (Nord's) way."

As he said that, a teacher was discussing with the exam next to him, and began to write and draw on the straw paper for Xu Heng's question.

Xu Heng, "???"

What the hell?

For the first time, after someone asked a question, there was silence below.

Xu Heng looked at Zhu Tiesen.

Zhu Tiesen just smiled and didn't have any opinion at all.

Stop laughing!

Comment?

Fortunately, not long after, someone questioned, "The title is a very good proof question, but..."

Just what?

Xu Heng looked over, "Is it just too difficult?"

"This question is difficult for us!"

"This is a typical question that looks easy but makes people unable to get started!"

"Maybe some students know how to do it, but they will also be frightened by the huge proof data that will follow!"

A professor stood up, "Indeed! But this question can be used in the last few questions of the entire test paper!"

"This works!"

"Ok, Ok!"

"..."

Everyone looked at each other in blank dismay, probably having their own answers in their hearts.

"Student Xu Heng will really give us problems, it seems that we can't fish in troubled waters!"

"Such a good topic has come out, we have to hurry up and find the topic!"

Topics are limited.

Once it is voted through, it means that it will be used in the test paper and the students will be tested.

The chances of other examiners' questions appearing in front of the examinees are even smaller!

Zhu Tiesen, "Everyone! Let's vote!"

"Agree, or disagree?"

Scan the audience...

The result of the vote on Xu Heng's question...

PS: Thank you [the other party is typing....] [月ミ] [tail number 0102] for your support!

New Year's Day is coming!Rich peach blossoms are always around you!

Ask for all support!The little author continues to explode!

Ask for automatic subscription! .

Chapter 140

The Olympiad competition is divided into preliminary rounds, semi-finals and finals.

There are multiple-choice questions, fill-in-the-blank questions, and answer questions in the preliminary round.

The topics of the semi-finals and finals are even more hard-core.

Originally Xu Heng thought that these ten days would pass very long, but he never expected that it would pass quickly.

In the examination room, these professors are brainstorming for the topic every day.

Even on the basis of other teachers' questions, they were revised and voted on.

The other party was not angry, and instead voted for the other party.

Here, everyone has a broad mind.

Because they have a common goal.

Xu Heng's questions were also passed one after another.

"Sometimes I wonder if you take special care of me."

Everyone became serious, "This is not a joke! We shoulder the responsibility of testing the candidates! Student Xu Heng, you have strength, and those who are capable are the ones who are capable. Don't belittle yourself."

A professor had a distressed expression, "I'm really sweating for this year's candidates!"

"Student Xu Heng's question is very tricky!"

"The preliminary round can make the candidates feel deep malice..."

Xu Heng, "Eh... this is not all approved by your vote!"

Zhu Tiesen and other professors finally sealed up the sample papers of the preliminary competition and handed them over to the official staff of the Mathematical Olympiad.

"Preliminary test papers are done! Come on everyone!"

"There are not enough questions in the test papers for the semi-finals and finals!!!"

Everyone continued to work hard!

Keep filling the quiz!

The questions presented should also be different from the real questions of the Mathematical Olympiad in previous years, not to mention, but also different from the question types of the preliminary round.

They are racking their brains!

Xu Heng felt relaxed.

Several professors including Zhu Tiesen told Xu Heng that he could let go of the questions, because the semi-finals and finals were more difficult, so Xu Heng began to let himself go.

but--

All the professors were dumbfounded after reading Xu Heng's question.

"Student Xu Heng, quickly accept your supernatural powers!"

"Your topic is beyond the outline!"

Xu Heng, "???"

"Super-classification? Professor Zhu Wei, there is also super-classification for Olympiad questions?"

Zhu Tiesen's face was full of black lines, "We must have a certain degree, don't we? Which of your classmates can solve these questions?"

"Even if you use your questions, it's not a big deal for these candidates to cry when they are tested! If it is serious, they may be depressed!"

"Think twice!"

"We don't want to compare between 0 points and a few points in the final!"

"Isn't this like choosing the taller among the dwarfs?"

　　Several of Xu Heng's questions were rejected on the grounds that they were "too difficult".

Zhu Tiesen comforted Xu Heng, "Don't be sad, don't be sad...it's my fault too! If I hadn't told you, let go, you wouldn't be like this..."

Xu Heng waved his hand, "Forget it, you guys go out, I'll just take a look!"

Zhu Tiesen, "Why don't you do this! Let's create a problem, how about you try to give yourself some ideas for solving the problem?"

"It's suitable, we will use yours!"

"That way, you won't be bored!"

"Everyone, what do you think of my proposal?"

Everyone agreed, "Yes! Student Xu Heng, don't refuse!"

"I agree!"

"Agree!"

"No problem!"

Xu Heng had black lines on his face.

You guys are clearly trying to find out about me!

Zhu Tiesen, "Student Xu Heng, please don't refuse!"

Xu Heng, "Uh..."

Zhu Tiesen, "Come on, let's start the topic!"

A professor ran to the blackboard enthusiastically, "I'll come! I'll come first!"

You are a professor!

Be steady, okay?

topic:

{Zn} (n≥1) is a sequence of complex numbers, the odd number items are real numbers, the even number items are pure imaginary numbers, and k∈N+, 丨ZkZ(k+1)丨=2(k power), record fn=丨Z1+ Z2+…+Zn丨

(1) Find the minimum possible value of f2020

(2) Find the minimum possible value of f2020*f2021

There are not many topics, and it looks like that, but it is different when it is done.

Everyone's first reaction was not to look at the professor's idea, but to look at Xu Heng.

Xu Heng, "Eh...don't all look at me! Watch the professor's answering process! Don't, don't..."

But even this professor said, "Don't give me face, come! Student Xu Heng, please!"

Xu Heng, "%￥#@￥..."

This question is not difficult for Xu Heng.

Anyway, it's hard to get off the tiger.

Then have a good time!

Standing up, thinking briefly, and after going through the process in his mind, Xu Heng said: "Assume an=Z(2n-1), bn=(Z(2n)/i(n=1,2,...)..."

"..."

"So in the end f2020=2..."

"Second question, order..."

"..."

"So the minimum value of these two multiplications in the end is 2 to the 1011th power."

Xu Heng spoke quickly!

It's useless to play straw paper!

It is said step by step from the mouth!

It’s the square under the root sign, it’s various absolute values, it’s Cauchy’s inequality, and so on...