Teachers, "!!!"
Hong Jingjun narrowed his eyes and laughed, "Student Xu Heng, tell me!"
"I know you have a way!"
All the teachers suddenly looked at Xu Heng excitedly.
Xu Heng looked at the crowd, he always felt that he was being led into the pit again.
"Hey... let's do it!"
Xu Heng had no choice but to simply say, "Facing the final question, I think candidates should know the importance of [translation] [specialization] and [focus on the target]!"
Some teachers couldn't bear it and asked, "What is [translation]? Be more specific!"
Xu Heng shrugged, "It's actually very simple. When we encounter Chinese, we often need to [translate] them into the language of mathematics."
"The [combination of numbers and shapes] that you often hear is actually a kind of [translation]. With the help of rectangular coordinates, geometry can be [translated] into algebra, and algebra can also be [translated] into geometry."
Everyone nodded, "We understand what you said, and we mentioned it to our classmates repeatedly during the lecture!"
Xu Heng hit the nail on the head, "But you only said it when necessary!"
"It's as if there are ten questions, and five questions need graphic assistance, so you can talk about these five questions!"
"It's not clear when they are the finale, use it!"
"Or, you didn't train them for the finale at all."
"It's that simple."
The teachers were silent.
Xu Heng talked about this from the standpoint of a student, and it was very thorough.
The leader of the mathematics group thought for a while, "Then this [specialization] should be based on the constraints of the topic or options, take some special values or special formulas, look for special laws, and then generalize them. Difficult questions can be guessed with specialization.”
Xu Heng nodded.
"What about the third one?" Some teachers couldn't wait.
Xu Heng, "." First of all, the goal is what you are asked to solve in the problem. Focus on the goal, that is, the problem you are solving, to associate the relevant theorems, properties, formulas, and connect with the known problems to solve the problem. , sometimes you can use the fixed target association formula to make reasonable guesses in difficult problems. "
After saying that, Xu Heng took the pen and paper.
Write down a question directly:
Define the geometric sequence whose first term is 1 and whose ratio is a positive number as "M-sequence".
(1)已知等比数列{an}(n∈N*)满足:a2a4=a5,a3-4a2+4a1=0,求证:数列{an}为“M-数列”;
(2)已知数列{bn}(n∈N*)满足:b1=1,(1/Sn)=(2/bn)-(2/B(n+1)),其中Sn为数列{bn}的前n项和。
①Find the general term formula of the sequence {bn};
② Let m be a positive integer, if there is an "M-sequence" {cn} (n∈N*), for any positive integer k, when k≤m, ck≤bk≤c(k+1) holds true, Find the maximum value of m.
The topic comes at your fingertips.
All the teachers were surprised and even curious, "Xu Heng, you don't know how to fill your head with question banks!"
"Why do you answer a question! Don't you even think about it?!"
Xu Heng smiled, "Teacher, let's read the questions!"
"These are not worth complaining about!"
Teachers, "%%####%..."
Look, is this still a human language?
Xu Heng, do you know what you are talking about?
Not worth it?
What else is worth it!
Your indifferent attitude is really reconciled.
Seeing the resentful expressions of the teachers, Xu Heng immediately waved his hands and changed the subject, "Look at the questions and questions! Everyone!"
He bluntly said, "Combine the goal with the known, and associate the relevant theorems, definitions, and methods."
"In some topics, we also need to constantly transform the target to better combine with the known, that is, to focus on the target needs to be used repeatedly."
"In addition, with a well-designed question, the conclusion of the previous small question can be used as a theorem in the latter small question."
"Therefore, this question transforms the goal, which can be transformed (the King's) as: Prove that the first item of the geometric sequence {an} is 1, and the common ratio is greater than 0, and use the properties of the geometric sequence to simplify the known... "
Many math teachers followed Xu Heng's train of thought to answer this question, and found that the first question, after transformation, can be easily proved!
"hiss……!"
"It seems that it is really solved!"
"If you think about this aspect of the test, the difficulty factor of this question will plummet."
"In this way, it will be more intuitive!"
"Student Xu Heng! You are really talented!"
"!!!"
Xu Heng was just talking about the process in such a hurry to divert everyone's attention, but it feels a bit outweighed by the gain.
After all, during the process of his narration, the enthusiasm of these teachers for him was even higher!
Some people's eyes are full of fire!
Xu Heng pouted, "%¥#@#¥%..."
He felt that this group of math teachers would definitely pester him.
Bite the bullet, Xu Heng continued talking.
For the three-step method he casually mentioned, use this question to explain one by one.
"We try to use n as some specific value to observe the changes in the last few items. This is a specialization..."
"..."
"Afterwards, stare at the target again, and continue to associate... the bow"
"..."
"For the second question of the second small question, the first thing to do is to translate Chinese into the corresponding mathematical language..."
"There is {cn}, when k≤m, make this formula constant, and find the maximum value of m. This logic is more complicated and abstract, and we need to use specific examples."
"Our goal is m, try to take several specific values for m, m is equal to 1, equal to 2, equal to 3..."
"..."
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Chapter 285
"Through the specialization here, we can find that, for some positive integer m..."
"..."
"In this way, our goal is transformed into the problem of finding the best value."
"..."
"So similar..."
"Then ask for guidance."
"..."
"So, when k is less than or equal to m, ck is less than or equal to bk is less than or equal to c(k+1), and m is less than or equal to 5."
"So, the maximum value of m is 5."
After Xu Heng said this, he looked at everyone, and they were all dumbfounded.
Xu Heng, "???"
Until the end of the meeting, the shock of these people still echoed in their minds.
End of the meeting.
Xu Heng returned to the hotel.
Accompanied by Sun Jianhua and Hong Jingjun.
Xu Heng wiped his cold sweat, "Fortunately, I ran quickly at the end of the meeting, otherwise I don't know when I will be back!"
Hong Jingjun smiled, "Who made you show so many extraordinary qualities?"
Xu Heng frowned, "Does that count?"
Hong Jingjun, "Puff..."
Sun Jianhua grinned instead.
"I said Lao Hong, you are asking for trouble!"
During dinner, Wu Liubai and Zhao Gensheng came over.
"Old Sun, Old Hong."
They know each other.
Hong Jingjun, like Sun Jianhua, called Wu Liubai, Xiao Wu.
At the dinner table, five people ate, drank, talked and laughed.
Wu Liubai came to see Xu Heng this time not only to take a look at him, but also because of Kevin's affairs.
Speaking of Kevin, Wu Liubai explained the situation to Xu Heng face to face.
Xu Heng, "Professor Wu said so, I really didn't think much about it."
"And I can also see how much this Professor Kevin likes the thin gold body."
"It's just that I didn't expect that those foreign university alliances were so optimistic about Professor Kevin."
"Isn't he retiring in two years?"
"Why are so many university leagues still looking for him?"
Wu Liubai, "Because of his importance!"
"He has been in our country for so many years, with him as a golden signboard, isn't the classmate in our country flocking to him?"
"In recent years, especially in recent years, more and more Chinese students have gone abroad, and fewer and fewer have returned."
"This has become a serious problem..."
"..."
When these things were mentioned, the atmosphere became dull.
Wu Liubai kept sighing as he spoke, but when he looked at Xu Heng, a smile appeared on his face again.
"And, these years, foreign countries have been attacking our education system!"
"It has always been difficult for us to have professional breakthrough students appearing to ask the breakthrough 060, and the clamor of the Russell University Group is the loudest!"
"But now, your appearance has completely deflated the Russell University Group!"
"Based on what I understand, they are actually learning about our education model while they are attacking us."
"Kevin understands our educational model very well."
"So, considering various reasons, he is now abroad and very popular."
Wu Liubai paused for a moment, his eyes fixed on Xu Heng.
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