Chapter 15 How do you prove it?

"Not just from one plus to one hundred, as long as the properties are comparable, i.e., the difference between two adjacent numbers is equal, it can be calculated in the same way, multiplying the sum of the first term plus the last term by half of the number of terms. Pen | fun | pavilion www. biquge。 info”

The story of Gaussian summation is to derive the following more complex summation of proportional numbers, in fact, it is not complicated to express and derive it with mathematical formulas, but there are no Arabic numerals in this world, let alone symbols that symbolize the common ratio and how many powers, and must be completely described in words.

"I didn't understand what you said, but what if the number of terms is singular, the addition of several numbers ends up with an extra 'half', where does this 'half' come from, everyone knows it's wrong. Hou Deyi grasped what he considered to be a fatal flaw and smiled triumphantly.

Even if he didn't ask Su Chengye what he had to say, "The number of items is single, and the sum of the first item and the last item must be double." The difference between two numbers is equal, and their difference can be called a tolerance, then the number of the last term is the multiple of the first term plus the tolerance, and the multiple is the number of terms minus one. If the number of terms is single, the multiplier must be double, and the multiplier multiplied by the tolerance is also double. The sum of singular and even numbers is singular, and the sum of even and even numbers is even, that is, the first term is singular and the last term is single, the first term is double, and the sum of the first term and the last term must be double. ”

Everyone frowned and thought, as if ...... There is some truth.

Hou Deyi silently tried a few times in his heart, and it was true, there was no reason for more "half", but how could he admit defeat.

"I don't have time to find the accounting room, I can't verify whether what you say is right or wrong, just assume that it's right, but what does it have to do with my question, I asked you to count the rice grains on the chessboard, but you are talking about the students in the school, the bull's head is not the horse's mouth. ”

The pen and paper have been delivered, and Su Chengye is very happy after reading it, the pen is not the brush he imagined, similar to a pencil, it is two thin strips of wood with an ink block between them.

He didn't rush to write, and continued: "The addition of multiple numbers seems cumbersome and complicated, but in fact, as long as there is a correlation between the numbers, they can be solved in an ingenious way. The grains of rice on the chessboard are added from the first grid to the 324th square, and I call their sum a and, a b, c, and d. Suppose that there is a sum of B, which is added from the second square of the chessboard to the 325th square, and I know that there is no 325 squares on the chessboard, which is just a hypothesis, which is convenient for calculation. ”

"The second cell is twice as large as the first, the third cell is twice as large as the fourth, and the third hundred and twenty-fourth cell is twice as large as the one hundred and twenty-four in the 325th format, that is, B and sum are twice as large as A, and you have no objection to this, right?"

The crowd shook their heads.

From the beginning of the disaster relief meeting, the center of the venue was Su Chengye, but everyone had all kinds of thoughts before, and at this time, the entire venue was dominated by Su Chengye, and even Shu Ziyu, the magistrate who presided over the disaster relief meeting, was attracted by his wonderful talk.

Zhong He's eyes that have not changed for thousands of years like a glacier are shining, such a strange story, such a wonderful number of skills, she has never heard of before.

"Adding from the second cell to the 325th cell, minus adding from the first cell to the 324th cell, is the 325th cell minus the first cell, which is also the value of B and minus A. ”

"There are a total number of rice grains on the chessboard, and you don't have to add more than 300 numbers to the cumbersome number, just calculate how many rice grains there are in the hypothetical 325 squares, and then subtract the first grain of rice. ”

Su Chengye began to calculate, his mouth was not idle, "This method can not only calculate the rice grains on the chessboard, it can calculate the sum of multiple numbers with multiples equal to any adjacent number, I call their multiples the common ratio, the ratio of proportions ......"

He spoke very slowly, and the main focus was on calculations, but everyone listened carefully, sometimes frowning, sometimes suddenly realizing, and then frowning, no one urged and raised objections, but there were many older people who thought he was too fast and their brains could not keep up.

It took hundreds of sheets of paper to finish, and I was sweating all over my head, and for the first time, I realized that doing math problems is also a physical task. In fact, he can calculate faster with an abacus, but he is not good at using an abacus, and he is worried about making mistakes, and he has always relied on the calculator for calculations.

"When the 'Tree of the Dao' computer was planted, the first thing I did was to make a calculator. ”

"There are three, four, one, seven, five ...... on the chessboard"

Su Chengye reported a number of ninety-seven digits, no one could verify the truth or falsehood, and no one cared, everyone was attracted by his simple summation method, they felt for the first time that the number was so wonderful, there were obviously more than three hundred numbers, and he made a hypothetical sum of B, and there were only a few numbers left after the reduction.

"You think that you can get away with a strange talk," Hou Deyi saw that the symbols he left on the paper were even stranger than the talismans drawn by Taoist priests, and they must have fooled people, "How do you prove that the answer is correct." ”

He went from the summation of the equal difference series to the summation of the equal ratio series, and deduced the summation formula in as concise language as possible, and finally won everyone's recognition, thinking that Hou Deyi could not make things difficult for himself in the process, but he underestimated the other party too much.

The calculation method is much simpler than before, the process has been reduced to less than one percent, and there are still computable processes, how can the calculation be proved to be correct? He could not prove it, because no one but him could understand Arabic numerals.

Zhong He was indignant for him, he proposed a new way of calculating, which is of great significance, the result of the calculation is no longer important, it is meaningless, Hou Deyi is so shameless how to have a little "adult" temperament.

No one spoke for Su Chengye, and everyone recognized in their hearts that Su Chengye was not only good at couplets, but also proficient in mathematics, but this could not be a reason for the disobedience of the county Chengda.

Zhong He never thought about this, she said it when she wanted to speak, and if she didn't want to say it, she didn't say it, and was about to express her support for Su Chengye, when a vision appeared in the sky.

The sky was clear, a few thin clouds were floating, the top of the clouds, a mountain peak flickering, a mirage like an ethereal, and so real in everyone's eyes. This scene is so familiar, and it is so unfamiliar, familiar because everyone has seen it, and strange because it was only seen by active communication before.

Communicating with the Puzzle Peak is like a dream when you are awake, what you see belongs to them, and others can also communicate with the Puzzle Peak, but even if you look at the same content, there are subtle differences from person to person.

Now the Puzzle Peak is in the sky, and it can be seen whether it is active communication or not, and everyone sees the same scene.

Hou Deyi's question and Su Chengye's answer appeared in the Puzzle Solving Peak, and they also found that Shu Ziyu, the county magistrate, forgot to add a Linglu reward for "Solving Confusion", but at this time, it was all trivial and no one paid attention.

More than 300 pairs of eyes at the venue of the Disaster Relief Conference stared at the Puzzle Peak, and tens of thousands of eyes in Sufeng County looked at the Puzzle Peak, they were all waiting, their hearts beating faster and faster, waiting for the next exciting scene.

There are no rewards for some "puzzles", but answering such "puzzles" is not necessarily fruitless. Questions that have never been asked before, or answers that have not been thought of before, once proven to be successful, the Puzzle Solving Summit will have an additional Spiritual Dew reward.