Chapter 28: I am studying the Goldbach conjecture
"Qin Luo, get up and talk about your process of solving this problem." Just then, Li Wei's "kind" words brought Qin Luo back to reality.
Let Sn be the first n items of the arithmetic sequence {an} and always a1=-7S3=-15
(1) Find the general term formula of {an}.
(2) Find Sn and find the minimum value of Sn.
This is an arithmetic minimum problem.
The first one is relatively simple, just find the general term formula, but the second one is more difficult.
Not only the value, but also its minimum value.
Teacher Li, this is to create an opportunity to make me pretend.
He is a rare teacher in a century.
At this moment, in Qin Luo's eyes, Li Wei was no longer a black-faced evil spirit, but a little white flower without sadness.
Qin Luo went to the blackboard and picked up the chalk and didn't answer immediately. He fell into deep thought.
Which method should I use to pretend?
Five minutes later, Qin Luo did not write a word, he stood in a daze at the blackboard.
"Qin Luo!" Li Wei's face was pale, he scolded, "What are you waiting for."
"Emmm, I'm thinking of using that method to solve it."
"Why, do you have several methods?" Li Wei came to be interested. For the arithmetic sequence, the knowledge of high school covers a solution. He was curious about what solution Qin Luo could "invent".
"Not much, not much, only three."
"..."
"The first kind." Qin Luo raised his hand and wrote a capital one on the blackboard, and then quickly began to solve the problem.
"Suppose the tolerance of {an} is d, and from the question, 3a1+3d=-15"
From a1=-7, d=2
So the general term formula of {an} is an=2n-9
(2) Sn=n²-8n=(n-4)² in (1) So when n=4, Sn is the minimum value and the minimum value is -16
"The second kind"
Without stopping, Qin Luo continued to write.
"F＇(ξ)*(b-a)=f(b)-f(a)……The minimum value is -16"
"The third kind of general term formula is an=2n-9......"
one two Three!
The three methods give exactly the same results!
But each method is completely different.
Quiet, deadly quiet.
Of the 47 students in the entire classroom, no one spoke.
It's not that they don't want to say, but they have nothing to say!
Qin Luo is in a tyrannical mess, and even the content of the university is useful, can they talk about it?
You know, knowing it is once, and using it flexibly is another.
Qin Luo can use university methods to solve problems, which proves that he is already thoroughly familiar with methods.
"The last method you used the method of subtracting items?" After a long period of silence, Li Wei broke the silence in the classroom.
"En." Qin Luo nodded.
"Where did you learn it."
"Self-taught."
"Where did you learn?" Li Wei asked, the split term elimination method, which is the content of the university and is slightly involved in the high school elective textbooks.
"Lagrange's median theorem, and Ptolemy's theorem,"
Li Wei was stunned: "Are you learning "High Mathematics" by yourself?"
"Well, but I'm studying Goldbach's conjecture recently."
Qin Luo coveted him for 500 points of Xueba points.
"..." The first second, Li Wei was still excited, but the next second he was speechless as if he had eaten a fly.
Goldbach guessed that it could be studied by a high school student. Do you think you are Tao Zhexuan or Qiu Chengtong?
