The strongest pilot ever
Chapter 21 Reciprocal Transformation of Binomial Coefficients
Chapter 21 Binomial Coefficient Reciprocal Transformation
21 Reciprocal transformation of binomial coefficients
Combinatorial Mathematics?
Analytical mathematics?
Fade Chen was stunned.
Why is this Yang Dong so awesome?Can even this kind of thing?It's not human at all!
He actually knew that Yang Dong was very powerful, but he didn't expect this guy to be so powerful.
It seems that he will have to work harder in the future.
The gap between them and him is the distance of a galaxy. Even if he has a system, he can't be conceited or self-righteous!
Must work harder!
Fade Chen secretly said to himself.
He quickly led his team members to start training in full swing.
As for Yang Dong, he had no choice but to take his people and leave in despair. This time, they fell behind again.
Can't go on like this!
It can't go on like this!
Yang Dong narrowed his eyes and said silently in his heart.
What Chen Fei said just now not only boosted the morale of their group, but also hit the morale of the members of their group.
Among the students who entered the experimental class, which one does not want to become better, and which one does not want to fly to the J-20 as soon as possible, so as long as it is a method that can make yourself go further, everyone is willing to give it a try!
But judging from the current situation, Fade Chen's group has indeed made greater progress, that is to say, Fade Chen's methods are indeed more effective!
"It will be difficult to lead the team if this continues!" Yang Dong secretly sighed.
Therefore, this cannot continue like this, and changes must be made immediately.
"So, what should I do?"
Yang Dong fell into deep thought as he walked.
The physical fitness assessment at the end of August, judging from the present, the members of their group are not a big problem. Everyone is the best of the best when they are selected, and the physical fitness assessment is not too difficult for their group of pilots, because The physical training at this time is mainly based on basic physical fitness, such as 3000-meter push-ups. Therefore, Yang Dong estimates that 90.00% of the people in this assessment will get full marks.
All of them are [-] points, so there is no way to tell whether one is strong or weak!
Therefore, we must change our thinking and work hard where we can distinguish between high and low.
I have to admit that Fade Chen really has a set of physical training, so I can no longer compete with him in this direction, I have to change my mind!
Moreover, relatively speaking, physical fitness is not Yang Dong's best field.
"Yes, give him a hard time in professional study!" Yang Dong quickly made a decision.
During the college entrance examination, his test score was more than 700, but Fade Chen only had 630. The gap is not usually big. From this point, it can be seen that Fade Chen is really not good at studying, at least not as good as him.
"Yes, just trample him to death in studies! I must let our group crush theirs!" Yang Dong let out a long breath.
at this time.
Chen Fei is leading everyone to train in full swing.
He explained while demonstrating: "Attention everyone, there are three ways to start a spiral ladder. The first is to start by stepping on the ladder. The essentials of the action are to hold the ladder column with both hands, push the bottom bar with one foot, and kick the ground with the other foot. After starting, kick the ground Hang your legs on the lower bar, extend your hands into the ladder from both sides, turn your wrists to hold the upper bar, and pin your toes to the ladder pillar or the bottom bar;
The second is to push the ladder to run up and start.Action essentials: stand at the bottom behind the ladder, hold the lower end of the ladder column with both hands, lift the ladder up to the top of the head, then push the ladder forward with both hands, run forward with the ladder, move up with both hands to hold the ladder column at an appropriate position, when running past the vertical part , jump up with one foot kicking hard, and the other foot on the bottom bar. When swinging back to the highest point, step over the bottom bar with the kicking leg, keep the toes away from the bottom bar, extend your hands into the ladder from both sides, and turn your wrists to hold on the bar;
The third is to jump start.Action essentials, the protector holds the ladder at an appropriate height and faces the practitioner."
Fade Chen's explanations are very careful, and he has done many demonstrations. In addition, he is not a teacher, so the students don't have so much fear in their hearts, so the learning progress is very fast. After a while, everyone basically mastered it.
He trained a group of people to death, and naturally picked up a lot of attributes.
The days just go by day by day.
For the entire month of August, everyone spent intense training and learning.
August focuses on military training, but not all physical training, but also professional knowledge learning.
However, because of our identity as an experimental class, our professional knowledge learning is different from that of ordinary students. Unlike ordinary classes, the teachers do not arrange the teaching progress uniformly. Each of their courses will have a teacher in the classroom, but he Only half of the time is taught, and the rest of the time is left for self-study and questions, and if you have any questions, ask questions.
That night, everyone gathered in the classroom and listened to the math teacher's lecture, but the teacher stopped talking halfway through, leaving time for everyone.
"Students can ask any questions." The mathematics teacher looked at everyone.
"Teacher, I have a question I want to ask you!" Yang Dong stood up first.
"What's the problem, you say?"
"Teacher, I want to ask you a question about reciprocal conversion of binomial coefficients." Yang Dong said.
Binomial Coefficient Reciprocal Transformation?
The teacher was stunned for a while, and the other students in the classroom were also stunned for a while.
It seems that you have never heard of the reciprocal transformation of the binomial coefficient, right?What a problem!
At this time, everyone's mathematics is still at the stage of advanced mathematics. For this stage of mathematics, most of these students in the classroom have already learned more than half of it by themselves, and some of them are quite good.
But even most of the most powerful candidates seem to have never heard of the reciprocal transformation of the binomial coefficient!
So everyone was taken aback.
After returning to their senses, many people couldn't help being shocked: "Fuck, is Yang Dong's math ability already so powerful? This shouldn't be about advanced mathematics, right? Could it be that he has already learned other mathematics fields by himself?" ?”
Swah——
Everyone looked at Yang Dong together.
But Yang Dong just looked at the teacher softly with a smile on his face.
At this time, the math teacher had recovered, and he quickly asked: "You are talking about a problem that is extremely important in the research fields of combinatorial mathematics, analytical mathematics, etc., and has attracted the attention of many scholars?"
"Yes teacher!" Yang Dong nodded.
"Okay, then tell me, what is the specific problem."
"What I want to ask is the Lehmer series identity." Yang Dong said.
He and the teacher asked and answered questions, talking freely.
All the students in the classroom were stunned-forced!
I dont understand!
Everyone has just learned advanced mathematics, but Yang Dong has already learned combinatorics and analytical mathematics!
No wonder this guy got such a high score in the college entrance examination!
It really is awesome!
The experimental class is really full of hidden dragons and crouching tigers.
Everyone couldn't help feeling secretly.
The teacher communicated with Yang Dong for about five or six minutes, and they both fell silent suddenly, because a question Yang Dong asked stumped the teacher.
It was extremely quiet in the classroom.
At this moment, Chen Fei, who had been sitting still, stood up: "Teacher!"
The math teacher turned to look at Fade Chen.
"Teacher, I suddenly had an idea about the issue you discussed just now, can you tell me?"
"You said."
"In general, the sum of the binomial coefficient reciprocal series is expressed in integral form. Obviously, the sum expression of the given series is not in closed form. So I think we can use the famous Lehmer series identity to construct For the new reciprocal series of binomial coefficients, the Lehmer series is organized into a standard series first, and then a batch of new reciprocal series of binomial coefficients are constructed by using the method of splitting the standard series, and their denominators are respectively Containing 1 to 4 odd factors and the product expression of the binomial coefficient, if we continue to use the split term method for this function, we can get the reciprocal series of the binomial coefficient with the denominator containing 5, 6, 7 ... P factors."
Fade Chen talked eloquently and expressed his thoughts.
The math teacher frowned at first, but after listening for a while, his eyes suddenly brightened, and his face flushed.
After Fade Chen finished speaking, he immediately said: "Fade Chen, come up and write down your derivation process!"
"Good teacher."
Fade Chen then walked to the podium, picked up the whiteboard marker handed to him by the teacher and began to write.
In the classroom, the students were dumbfounded again.
Yang Dong was also dumbfounded!
Mom - forced!
Originally, he wanted to take this opportunity to show off his mathematical talents and step on the other party, so he quietly studied combinatorics and analytic mathematics for several days in private, and finally found a person who can ask questions. Mathematics teacher's question, in order to show their strength.
If what happened tonight is successful, everyone will say this about him in the future, "Look, that's Yang Dong, a math freak, the freak who asked all the math teachers down."
But now
After a lot of hard work, I made wedding dresses for others!
He really knocked the math teacher down!
But the solution to that question - a question he didn't know how to answer - was answered by Fade Chen!
But how is this possible?
Isn't Fade Chen's professional ability very bad?
Why is he so strong?
He can figure out the problems that the mathematics teacher failed to understand at once!
Is this guy an alien?
Physically, he was beaten to pieces by Fade Chen. Now, even in terms of professional skills, he was defeated by the opponent!
In the days to come, how can I pretend to be forced to fly!
At this time, in Fade Chen's mind, a soft voice sounded again: "You once again hit Yang Dong's self-esteem, causing him to drop Russian*4, Taekwondo*3, and Material Mechanics*2. With a preliminary understanding, the Taekwondo skills have become higher, and the mechanics of materials have also gained a certain understanding.”
(End of this chapter)
21 Reciprocal transformation of binomial coefficients
Combinatorial Mathematics?
Analytical mathematics?
Fade Chen was stunned.
Why is this Yang Dong so awesome?Can even this kind of thing?It's not human at all!
He actually knew that Yang Dong was very powerful, but he didn't expect this guy to be so powerful.
It seems that he will have to work harder in the future.
The gap between them and him is the distance of a galaxy. Even if he has a system, he can't be conceited or self-righteous!
Must work harder!
Fade Chen secretly said to himself.
He quickly led his team members to start training in full swing.
As for Yang Dong, he had no choice but to take his people and leave in despair. This time, they fell behind again.
Can't go on like this!
It can't go on like this!
Yang Dong narrowed his eyes and said silently in his heart.
What Chen Fei said just now not only boosted the morale of their group, but also hit the morale of the members of their group.
Among the students who entered the experimental class, which one does not want to become better, and which one does not want to fly to the J-20 as soon as possible, so as long as it is a method that can make yourself go further, everyone is willing to give it a try!
But judging from the current situation, Fade Chen's group has indeed made greater progress, that is to say, Fade Chen's methods are indeed more effective!
"It will be difficult to lead the team if this continues!" Yang Dong secretly sighed.
Therefore, this cannot continue like this, and changes must be made immediately.
"So, what should I do?"
Yang Dong fell into deep thought as he walked.
The physical fitness assessment at the end of August, judging from the present, the members of their group are not a big problem. Everyone is the best of the best when they are selected, and the physical fitness assessment is not too difficult for their group of pilots, because The physical training at this time is mainly based on basic physical fitness, such as 3000-meter push-ups. Therefore, Yang Dong estimates that 90.00% of the people in this assessment will get full marks.
All of them are [-] points, so there is no way to tell whether one is strong or weak!
Therefore, we must change our thinking and work hard where we can distinguish between high and low.
I have to admit that Fade Chen really has a set of physical training, so I can no longer compete with him in this direction, I have to change my mind!
Moreover, relatively speaking, physical fitness is not Yang Dong's best field.
"Yes, give him a hard time in professional study!" Yang Dong quickly made a decision.
During the college entrance examination, his test score was more than 700, but Fade Chen only had 630. The gap is not usually big. From this point, it can be seen that Fade Chen is really not good at studying, at least not as good as him.
"Yes, just trample him to death in studies! I must let our group crush theirs!" Yang Dong let out a long breath.
at this time.
Chen Fei is leading everyone to train in full swing.
He explained while demonstrating: "Attention everyone, there are three ways to start a spiral ladder. The first is to start by stepping on the ladder. The essentials of the action are to hold the ladder column with both hands, push the bottom bar with one foot, and kick the ground with the other foot. After starting, kick the ground Hang your legs on the lower bar, extend your hands into the ladder from both sides, turn your wrists to hold the upper bar, and pin your toes to the ladder pillar or the bottom bar;
The second is to push the ladder to run up and start.Action essentials: stand at the bottom behind the ladder, hold the lower end of the ladder column with both hands, lift the ladder up to the top of the head, then push the ladder forward with both hands, run forward with the ladder, move up with both hands to hold the ladder column at an appropriate position, when running past the vertical part , jump up with one foot kicking hard, and the other foot on the bottom bar. When swinging back to the highest point, step over the bottom bar with the kicking leg, keep the toes away from the bottom bar, extend your hands into the ladder from both sides, and turn your wrists to hold on the bar;
The third is to jump start.Action essentials, the protector holds the ladder at an appropriate height and faces the practitioner."
Fade Chen's explanations are very careful, and he has done many demonstrations. In addition, he is not a teacher, so the students don't have so much fear in their hearts, so the learning progress is very fast. After a while, everyone basically mastered it.
He trained a group of people to death, and naturally picked up a lot of attributes.
The days just go by day by day.
For the entire month of August, everyone spent intense training and learning.
August focuses on military training, but not all physical training, but also professional knowledge learning.
However, because of our identity as an experimental class, our professional knowledge learning is different from that of ordinary students. Unlike ordinary classes, the teachers do not arrange the teaching progress uniformly. Each of their courses will have a teacher in the classroom, but he Only half of the time is taught, and the rest of the time is left for self-study and questions, and if you have any questions, ask questions.
That night, everyone gathered in the classroom and listened to the math teacher's lecture, but the teacher stopped talking halfway through, leaving time for everyone.
"Students can ask any questions." The mathematics teacher looked at everyone.
"Teacher, I have a question I want to ask you!" Yang Dong stood up first.
"What's the problem, you say?"
"Teacher, I want to ask you a question about reciprocal conversion of binomial coefficients." Yang Dong said.
Binomial Coefficient Reciprocal Transformation?
The teacher was stunned for a while, and the other students in the classroom were also stunned for a while.
It seems that you have never heard of the reciprocal transformation of the binomial coefficient, right?What a problem!
At this time, everyone's mathematics is still at the stage of advanced mathematics. For this stage of mathematics, most of these students in the classroom have already learned more than half of it by themselves, and some of them are quite good.
But even most of the most powerful candidates seem to have never heard of the reciprocal transformation of the binomial coefficient!
So everyone was taken aback.
After returning to their senses, many people couldn't help being shocked: "Fuck, is Yang Dong's math ability already so powerful? This shouldn't be about advanced mathematics, right? Could it be that he has already learned other mathematics fields by himself?" ?”
Swah——
Everyone looked at Yang Dong together.
But Yang Dong just looked at the teacher softly with a smile on his face.
At this time, the math teacher had recovered, and he quickly asked: "You are talking about a problem that is extremely important in the research fields of combinatorial mathematics, analytical mathematics, etc., and has attracted the attention of many scholars?"
"Yes teacher!" Yang Dong nodded.
"Okay, then tell me, what is the specific problem."
"What I want to ask is the Lehmer series identity." Yang Dong said.
He and the teacher asked and answered questions, talking freely.
All the students in the classroom were stunned-forced!
I dont understand!
Everyone has just learned advanced mathematics, but Yang Dong has already learned combinatorics and analytical mathematics!
No wonder this guy got such a high score in the college entrance examination!
It really is awesome!
The experimental class is really full of hidden dragons and crouching tigers.
Everyone couldn't help feeling secretly.
The teacher communicated with Yang Dong for about five or six minutes, and they both fell silent suddenly, because a question Yang Dong asked stumped the teacher.
It was extremely quiet in the classroom.
At this moment, Chen Fei, who had been sitting still, stood up: "Teacher!"
The math teacher turned to look at Fade Chen.
"Teacher, I suddenly had an idea about the issue you discussed just now, can you tell me?"
"You said."
"In general, the sum of the binomial coefficient reciprocal series is expressed in integral form. Obviously, the sum expression of the given series is not in closed form. So I think we can use the famous Lehmer series identity to construct For the new reciprocal series of binomial coefficients, the Lehmer series is organized into a standard series first, and then a batch of new reciprocal series of binomial coefficients are constructed by using the method of splitting the standard series, and their denominators are respectively Containing 1 to 4 odd factors and the product expression of the binomial coefficient, if we continue to use the split term method for this function, we can get the reciprocal series of the binomial coefficient with the denominator containing 5, 6, 7 ... P factors."
Fade Chen talked eloquently and expressed his thoughts.
The math teacher frowned at first, but after listening for a while, his eyes suddenly brightened, and his face flushed.
After Fade Chen finished speaking, he immediately said: "Fade Chen, come up and write down your derivation process!"
"Good teacher."
Fade Chen then walked to the podium, picked up the whiteboard marker handed to him by the teacher and began to write.
In the classroom, the students were dumbfounded again.
Yang Dong was also dumbfounded!
Mom - forced!
Originally, he wanted to take this opportunity to show off his mathematical talents and step on the other party, so he quietly studied combinatorics and analytic mathematics for several days in private, and finally found a person who can ask questions. Mathematics teacher's question, in order to show their strength.
If what happened tonight is successful, everyone will say this about him in the future, "Look, that's Yang Dong, a math freak, the freak who asked all the math teachers down."
But now
After a lot of hard work, I made wedding dresses for others!
He really knocked the math teacher down!
But the solution to that question - a question he didn't know how to answer - was answered by Fade Chen!
But how is this possible?
Isn't Fade Chen's professional ability very bad?
Why is he so strong?
He can figure out the problems that the mathematics teacher failed to understand at once!
Is this guy an alien?
Physically, he was beaten to pieces by Fade Chen. Now, even in terms of professional skills, he was defeated by the opponent!
In the days to come, how can I pretend to be forced to fly!
At this time, in Fade Chen's mind, a soft voice sounded again: "You once again hit Yang Dong's self-esteem, causing him to drop Russian*4, Taekwondo*3, and Material Mechanics*2. With a preliminary understanding, the Taekwondo skills have become higher, and the mechanics of materials have also gained a certain understanding.”
(End of this chapter)
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