1+2^35
Sn=a1(q^n-1)/(q-1)
Lin En used magic as ink to write out the formula represented by the grid game, then looked at the apprentices who had not yet recovered from the exponentially increasing terror, and said loudly.
"Why don't you write this formula down?"
Jonny and others hurriedly opened the page, picked up a quill pen and copied down the formulas that they couldn't understand at all. The dumbfounded Alok on the side was the best example, that is what will happen if you don't learn the Mathematical Olympiad. !
"Professor Lin En..." Alok looked at Lin En and shouted tremblingly, his eyes filled with tears, and he almost burst into tears.
"Alok, I just heard you say that you are good at math?" Linn asked.
I'm not, I didn't, don't talk nonsense...
Alok shook his head hurriedly and wanted to deny it, but Linn waved his hand and continued to speak.
"Well, as long as you can accurately calculate the total of these thirty-six squares of copper coins before class tomorrow, then this bet will be over!"
"Of course, you only have one chance to speak!"
Lin En glanced at the large amount of coins piled on the square table with a little pity, but had no intention of accepting them.
First of all, it was impossible for the other party to get the money, and secondly, it would be a bit too scary for him to let all the apprentices spend all their savings in just one game.
Who would dare to come to his Mathematical Olympiad class in the future?
Elok stared blankly at the floating magic fluorescence, completely unable to understand what these arithmetic symbols were. He even began to doubt whether he could count...
Peirce, who was still envious of Alok before, immediately became gloating about his misfortune. Fortunately, he hesitated, otherwise he would be the one making a fool of himself now.
Unexpectedly, Lin En changed his words, looked at everyone present, and continued to speak.
"Same for you!"
"If I remember correctly, when Alok borrowed money from you, he said [if he can fill all the squares, he will pay back double]."
"It's a pity that Alok failed to do this, so the promise is invalid. Not only will you not be able to get more gold coins, but the money you suppressed before will continue to be left with me!" Lin En reached out and picked up a few coins. Hirakata said playfully, looking at the gold, silver and copper coins on the table.
Hearing this, the Mathematical Olympiad classroom suddenly burst into mourning. Peirce and the others angrily kicked Alok, this kid is actually cheating!
Linn raised his voice a few points and pointed at the exponential summation formula floating in the sky. "There is an easy way to add exponential operations. If it were me, I would be able to calculate the sum of them in ten seconds if I knew the last number!"
"The task I give you after class is to find patterns and solve the formulas I wrote! When you get the answer, you can get the money back!"
Lin En looked around at the students who were holding quill pens and bowing their heads to calculate, and nodded with satisfaction. Only this kind of personal experience can make people truly feel the charm of the Mathematical Olympiad!
In addition, he is also using this game to find out the mathematical level of these apprentices.
Judging from Alok's performance, they have already learned the most basic algorithms. Maybe they can start teaching them from slightly more difficult formulas next time!
The two-hour Mathematical Olympiad class ended soon.
Although they did not learn any new magic, all the students, driven by the desire to get their deposits back, maintained a high degree of enthusiasm and even couldn't wait to share what they saw and heard in the class with others.
In just one day, the reputation of Professor Linn's square game has spread.
In order to let more people understand the charm of exponential growth, Lin En moved the square plate directly to the door of Iyeta College, and changed the square into a total of forty-nine squares with seven rows and seven verticals. A sign was erected on it and the rules of the bet were rewritten.
If anyone can fill these squares with the corresponding copper coins, he will give away the alchemical formula used to destroy Harbor Town.
That's right, you only need to start with one copper coin and fill it up according to the rule that the copper coins in the next grid are twice as much as the previous one. After filling in the money, you can even get it back. He doesn't have to pay a penny. receive!
At this time, not only the wizard apprentices, but also several professors in the college were tempted.
Is there such a good thing?
This kind of alchemical formula that requires a lot of preparation to explode with powerful power may seem troublesome, but it can produce special miraculous effects in some special occasions.
You must know that the power of this thing is comparable to five-ring or even six-ring magic!
In the evening, while the students were leaving school or returning to their dormitories, Professor Kevin sneaked up to the combined square tables and studied the rules on the square plates.
Does the number in each square double the previous one?
Kevin touched his chin and thought about it in his mind. Just as he was thinking about it, a familiar voice came from behind.
"Don't forget it, it's absolutely impossible to fill these squares!"
"Do you know how much savings I have? Professor Philip?" Kevin asked slightly dissatisfied, and he knew many good friends. Anyway, the money is only used to fill in the grid, and you can take it back after filling it in. The worst is not to worry about it anymore Borrow some.
Could it be that these squares are really as rumored, and that even all the wealth of the entire Iyetta Harbor cannot be filled?
Kevin scoffed at this statement. This rumor was simply too outrageous!
"Do you know how many copper coins are needed to fill in the last square of these seven rows and seven columns?" Philip said helplessly. "It's two hundred and eighty-one trillion!"
"Two million and eighty-one million copper coins, that's quite a lot..." Kevin was somewhat surprised, but after a pause, he suddenly realized that the unit Phillip mentioned seemed to be... trillions... billions?
"Wait, are you sure you're not mistaken?" Kevin was completely confused.
This was the first time he heard that there was a trillion unit.
"Of course not! I've verified it myself..." Philip said angrily. He was a little surprised when he heard the apprentices talk about it before, and then it took him a full nine sheets of paper to finish all the calculations, because those numbers were really Too long.
Kevin silently did the math in his head. Although it was just the simplest multiplication, the amount became larger the further he calculated it. Mental calculation alone was no longer sustainable, so he could only make a rough estimate first.
Based on the experience of the previous columns, the amount will increase about ten times every three to four squares.
There are seventy-nine grids in total, that is... at least one hundred trillion times!
Kevin couldn't help but take a breath, this kind of growth is really terrifying!
Not to mention the Iyeta seaport, even if the entire continent was emptied, it would be impossible to raise so much money!
Fortunately, he deliberately chose a time when no one was around to try it out secretly, otherwise he would probably make a fool of himself in front of the students.
Kevin secretly rejoiced in his heart, and then discovered that in addition to the rows of squares on the square table in front of him, there were also some strange characters carved on it.
Sn=a1{q^（n-1）}/(q-1)
"What are these runes? Some kind of magic symbols?" Kevin asked in confusion.
"This seems to be... the formula for the summation of a geometric sequence? It should be called this, right?" Philip said uncertainly, "Professor Linn said that as long as the last number is calculated, he can calculate these squares in ten seconds How many copper coins add up to."
"Can such a large amount of data really be calculated within ten seconds?" Kevin frowned.
"Master Heralam seems to have solved the meaning of this arcane mathematical formula!" Philip exclaimed, "In just one afternoon, you are truly worthy of being a great wizard."
"Did the master tell you what these Mathematical Olympiad symbols mean?" Kevin asked eagerly. After doing the exponential calculation, he found that this so-called Mathematical Olympiad seemed quite interesting.
"No..." Philip shook his head regretfully, "Master Heralam only asked me to come over and add a small reward to this game. Whoever can figure out the meaning of this formula first will get twenty magic gold coins. reward!"
As he spoke, Philip took out the gold coins and used magic to fix them on the square table.
…
At this moment, the person everyone is talking about, Lin En, the new professor of the Mathematical Olympiad class, is sitting leisurely on the sofa in the room, eating the dinner brought by the goblin while checking the "Basics of Magic" borrowed from the college library. Principle", "Elemental Magic Analysis".
Although the professor's life at Ieta College is very comfortable and does not feel the slightest crisis, Lin En will not slack off because of this.
Everything in the Wizarding Land is unfamiliar to him. Once he encounters any trouble, the only thing he can rely on is his own strength.
In addition, as a professor, he also had to acquire some basic magic knowledge.
However, these two books on the principles of magic written by legendary wizards made Linn's head look over the top, because the books were filled with a large number of such as [Serlu], [Enzesi], [Keze] and so on. He was completely confused about the vocabulary, so he could only verify it bit by bit based on the descriptions of these nouns in the book.
After spending more than three hours analyzing it, and combining it with his own understanding of magic after time travel, Lin En could barely understand the first half of the book.
First of all, his previous guess was not wrong. Wizards did release magic by manipulating, influencing, and mimicking elements.
However, the official wizard's ability is very limited. Not all elements can be controlled, and the accuracy is not enough. At least it cannot crush molecules or atoms. It can only perform simple arrangements and combinations.
"Hydrogen, oxygen, nitrogen, phosphorus..." Lin En silently thought about the four elements he had controlled, and several guesses emerged in his mind.
First, the difficulty of element manipulation may be related to the element cycle. For example, official wizards can only control the short-term elements in the first three columns of the periodic table, but cannot control the long-term elements in the fourth to seventh columns.
The second is determined by the number of nuclear charges in the element.
The third is to divide them by metal and non-metal elements.
On this point, Linn had done experiments before, trying to use zero-ring magic [primary material deconstruction] to disintegrate the steel sword in his hand.
It was clear that he failed!
No matter how hard Linn tried, the sword remained motionless.
This means that with the ability of a wizard apprentice or even a formal wizard, there is no way to directly affect the metal elements.
Of course, this is not necessarily true for great wizards and legendary wizards.
Because according to the records of "Basic Principles of Magic", [Basic Material Deconstruction Technique] also has two advanced magics.
They are the four-ring magic [High-level Material Deconstruction], and the seven-ring magic [Great Disintegration]!
It just so happens that the fourth and seventh rings are the dividing line between being promoted to a great wizard and a legendary wizard!
While thinking about it, Linn asked 071 to record these contents in the research file, and then turned to the second half of "Basic Principles of Magic", which contained even more mysterious descriptions of magic.
This legendary wizard regards magic as the origin of the entire universe, the most basic thing that makes up all matter, and the real power of creation!
"The origin?" Lin En frowned. Based on his observations these days, magic seems to exist in every corner of the world, but unlike elements, he can only perceive but cannot truly 'see' unless it is Only by using magic like [Magic Missile] can the magic materialize in a short time.
Forget it, this is obviously not something he can study clearly at his current level...
Lin En touched the pain in his head, decided to put this problem aside for now, and then opened "Detailed Explanation of Elemental Magic".
[Fireball], [Corrosion], [Louding Curse], [Touch of Ice], [Secondary - Fire Demon's Hand], [Pyrotechnic], [Toxic Field]...
The entire "Elemental Magic Analysis" records a total of seventeen kinds of magic from the first to the third ring.
Lin En's eyes glanced at the so-called second and third-ring magics for a few times, and then he stopped paying attention. Instead, he focused on the first-ring magics.
With the help of the power of his brain, although he can, as a wizard apprentice, complete magic mimicry, something that only formal wizards can do, he is limited to learning and using one-ring magic.
For example, the principle of the three-ring magic poison field is to use magic power to convert it into some kind of toxic gas, which may be chlorine or fluorine. In short, it is not an element that he can obtain in a short time.
If it cannot be analyzed, it cannot be converted and used. His mental power is far from enough to cover such a large range.
At close range, it is better to simply reduce or increase the oxygen content in the air, which can achieve a similar effect.
With his current abilities, learning and improving one-level magic is the easiest thing to do.
And one-ring magic can also be divided into ordinary and high-level.
The so-called high-level magic is actually a simplification of higher-level magic, or an enhancement of low-level magic.
For example, his [White Phosphorus-Fireball Technique] is strictly a first-level high-level magic. However, due to the extremely poisonous and indestructible properties of white phosphorus, it reaches the level of second-level magic in terms of power.
And another improved magic [White Phosphorus - Hand of Fire Demon] has a destructive power close to that of three-ring magic.
But Lynn is well aware of the limitations of white phosphorus fire.
Don't look at him using this thing to kill everyone in the Sekas Empire, and even killed Anjuk, who was comparable to a three-ring wizard.
Lin En knew very well that this thing was fine for bullying those uneducated bishops, but once it was used against wizards, its power would be greatly reduced.
After all, the two important characteristics of white phosphorus fire can be dealt with by formal wizards. Once the information is leaked, it will not be so easy to achieve good results.
Therefore, he must learn more magic to increase his trump card...
(PS: I want anything in the new book! Today I will post two chapters together. You can also discuss whether it is better to have more scientific principles or to keep it as simple as possible.)
