Chapter 28 I am working on the Goldbach conjecture
"Qin Luo, get up and talk about your process of solving this problem." At this moment, Li Wei's "kind" words brought Qin Luo back to reality.
Record Sn as the sum of 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 sequence minimum value problem.
The first question is relatively simple, just find the formula of the general term, but the difficulty of the second question suddenly increases.
Not only is the value requested, but its minimum value is also requested.
Teacher Li is creating an opportunity for me to pretend.
It is really a good teacher that is rare 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 sorrow or injury.
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 force myself?
Five minutes passed, Qin Luo didn't write a single word, he stood in front of the blackboard in a daze.
"Qin Luo!" Li Wei scolded with a livid face, "What are you waiting for?"
"emmm, I'm wondering which method to use to solve it."
"Why, do you have several methods?" Li Wei became interested. For the arithmetic sequence, the knowledge in high school only covered one solution. He was curious about what solution Qin Luo could "originally create".
"No more, no more, just three."
"..."
"The first one." Qin Luo raised his hand and wrote a capital one on the blackboard, then quickly started to solve the problem.
"Assuming that the tolerance of {an} is d, we can know from the question that 3a1+3d=-15"
d=1 from a7=-2
So the general term formula of {an} is an=2n-9
（2）由（1）的Sn=n-8n=（n-4）所以当n=4时Sn为最小值，最小值为-16
"Second"
Without stopping, Qin Luo continued writing.
"f'(ξ)*(ba)=f(b)-f(a)...minimum value is -16"
"The formula of the third general term is an=2n-9..."
one two Three!
Three methods, the results are exactly the same!
But each method is very different.
Quiet, deathly quiet.
There were 47 students in the entire classroom, but no one spoke.
It's not that they don't want to say it, but they have nothing to say!
This guy Qin Luo is so tyrannical that he even used the content of the university, can they talk about it?
You know, knowing it is one thing, and using it flexibly is another.
Qin Luo's ability to use university methods to solve problems proves that he has already mastered the methods.
"Did you use the split-term cancellation method in the last method?" After a long silence, Li Wei finally 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 cancellation method is the content of the university, and it is slightly involved in the elective textbooks of high school.
"Lagrange's Mean Value Theorem, and Ptolemy's Theorem,"
Li Wei was stunned: "Are you studying "Advanced Math" by yourself?"
"Well, but recently I'm studying Goldbach's conjecture."
Qin Luo coveted him for five hundred points of academic mastery.
"..." One second, Li Wei was elated, but the next second he was speechless as if he had eaten a fly.
Goldbach's conjecture is something that a high school student can research. Do you think you are Terence Tao or Qiu Chengtong?