I Made Scientific Magic

When q≠1

Sn=a1(1-q^n)/(1-q)

Lin En wrote out the formula represented by the grid game with magic power, and then looked at the apprentices who had not yet recovered from the horror of exponential growth, and said loudly.

"Why don't you write down this formula?"

Johnny and the others hurriedly turned the page, picked up a quill and copied down the formula they couldn't understand at all. Ai Luoke, who was stunned by the side, was the best example, that is the end of not learning the Olympiad !

"Professor Lynn..." Eloque looked at Lynn and shouted tremblingly, his eyes filled with tears, and he was about to cry.

"Eloque, I just heard from you that you are good at math?" Lynn asked.

I'm not, I'm not, don't talk nonsense...

Eloque shook his head hurriedly and wanted to deny it, but Lynn waved his hand and continued to speak.

"Well, as long as you can accurately calculate the sum of the thirty-six squares of copper coins before class tomorrow, then the bet is over!"

"Of course, you only have one chance to speak!"

Lin En glanced at the large amount of coins piled up on the square table with a little pity, but he didn't intend to accept them.

First of all, it is impossible for the other party to get the money, and secondly, it is a bit too scary to let a group of apprentices spend all their savings with a single game.

After that, who would dare to come to his Math Olympiad class?

Ai Luoke stared blankly at those floating magical fluorescent lights, completely unable to understand what these arithmetic symbols were, and he even began to doubt whether he could count...

Pierce, who was still envious of Elrock before, immediately became gloating. Fortunately, he hesitated for a while, otherwise he would be the one who made a fool of himself now.

Unexpectedly, Lin En's voice changed, he looked at the people present, and continued to speak.

"You too!"

"If I remember correctly, when Eloque borrowed money from you, he said [if he can fill all the boxes, he will return it twice]."

"It's a pity that Eloke failed to do this, so the promise is invalid. Not only will you not get more gold coins, but the money you have suppressed before must continue to be with me!" Lynn reached out and picked up a few gold coins. The gold, silver and copper coins on the square table, said playfully.

Hearing this, the classroom of Mathematical Olympiad was filled with wailing, and Pierce and the others stomped on Ai Luoke in anger. This kid is actually cheating!

Lynn raised his voice a little, and pointed to the exponential summation formula floating in the sky. "There is a simple way to do exponential addition. If it were me, if I knew the last number, I would be able to calculate their sum in ten seconds!"

"The task I give you after class is to find the law and solve the formula I wrote! When do you get the answer, and when will you get the money back!"

Lin En looked around at the students who were holding quills and bowing their heads to calculate, and nodded in satisfaction. Only this kind of personal experience can make people truly feel the charm of Mathematical Olympiad!

In addition, he is also using this game to find out the mathematics level of these apprentices.

Judging from Eloke's performance, they have already learned the most basic algorithms, and maybe they can start teaching with slightly more difficult formulas next time!

The two-hour Mathematics Olympiad class ended soon.

Although they didn't learn any new magic, all the students were forced by the idea of ​​getting their deposits back, and they maintained extremely high enthusiasm, and even couldn't wait to share what they saw and heard in class with others.

In just one day, the name of Professor Lynn's square game has spread.

In order to let more people understand the charm of exponential growth, Lynn directly moved the square plate to the gate of Iyeta Academy, and changed the square into a total of forty-nine squares with seven rows and seven vertical lines. 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 alchemy 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 large as the previous grid. receive!

This time, not only the wizard apprentices, but even several professors of the college were a little tempted.

Is there such a good thing?

This kind of alchemy formula that requires a lot of preparation to explode its powerful power may seem troublesome, but it can exert special miraculous effects in some special occasions.

You must know that the power of this thing can be compared to five-ring or even six-ring magic!

In the evening, when a group of students were leaving school or returning to the dormitory, plastic surgery professor Kevin sneaked up to the merged square table by himself and studied the rules on the square plate.

Does each square have double the number of the previous one?

Kevin stroked his chin, pondering secretly in his heart, and just as he was thinking, a familiar voice came from behind.

"Forget it, it is absolutely impossible to fill these squares!"

"Do you know how much savings I have, Professor Philip?" Kevin asked a little dissatisfied, and he knew a lot of friends. Anyway, the money is just used to fill in the grid, and you can take it back after filling it out. borrow a little.

Could it be that these squares are really the same as in the rumors, and it is impossible to fill them with all the wealth of the entire Iyeta Harbor?

Kevin scoffed at this statement, this rumor is 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 rather helplessly. "It's two hundred and eighty-one trillion!"

"2.81 million copper coins, that's quite a lot..." Kevin was a little surprised, but after a pause, he suddenly realized that the unit Philip was talking about seemed to be...billion...billion?

"Wait, are you sure you didn't make a mistake?" Kevin was stunned.

It was the first time he heard that there was a unit of trillions.

"Of course not! I've verified it myself..." Philip said angrily. He was also a little surprised when he heard the apprentices talking about it before, and then he used a whole nine manuscript papers to calculate all of them, because those numbers are really huge. too long.

Kevin silently calculated in his head. Although it was just the simplest multiplication, the amount became larger as he calculated it later. It was already a bit untenable to do mental calculations alone, so he could only make a rough estimate first.

According to the experience of the first few columns, the amount will increase about ten times for every three to four grids.

There are a total of forty-nine grids, that is... at least one hundred trillion times!

Kevin couldn't help taking a breath, this kind of growth is really terrifying!

Not to mention the Iyeta seaport, even if the entire continent is emptied, it is impossible to raise so much money!

Fortunately, he deliberately chose to sneak out to try when there was no one around, otherwise he would have made a fool of himself in front of the students.

Kevin secretly rejoiced in his heart, and then found that in addition to rows of squares, some strange characters were engraved on the square table in front of him.

When q≠1, Sn=a1(1-q^n)/(1-q)

"What are these runes? Some kind of magical symbols?" Kevin asked puzzled.

"This seems to be... the summation formula of geometric series? It should be called this?" Philip said uncertainly, "Professor Lynn said that as long as the last number is calculated, he can calculate these squares within ten seconds." How much do the 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 unlocked the meaning of this Olympiad formula!" Philip said with admiration, "It's only an afternoon. You really deserve to be Your Excellency the Great Wizard."

"Did the master tell you what these Olympiad symbols mean?" Kevin asked eagerly. After doing exponential calculations, he found that the so-called Olympiad seemed quite interesting.

"No..." Philip shook his head regretfully, "Master Hilaram only asked me to come over and add a small reward to this game, whoever can solve the meaning of this formula first will get twenty magic gold coins reward!"

While speaking, Philip took out the gold coins and fixed them on the square table with magic.

...

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 "Magic Basics" borrowed from the college library. Principle", "Analysis of Elemental Magic".

Although the life of the professor at Iyeta College is very comfortable and he doesn't feel the slightest crisis, Lynn will not slack off because of this.

Everything in the Land of Wizards is unfamiliar to him, and 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 catch up on some basic magic knowledge.

However, these two books on the principles of magic written by legendary wizards made Lynn's head big, because the books were filled with a lot of things such as [Thuru], [Enzexi], and [Keze], which made Lin En feel dizzy. The vocabulary that he can't figure out at all can only be verified bit by bit based on the description of these nouns in the book.

It took more than three hours to analyze, and combined with his little knowledge of magic power after time travel, Lynn barely understood the first half of the book.

First of all, his previous guess was not wrong, wizards did release magic through manipulation, influence, and mimicry elements.

However, the ability of official wizards is very limited, not all elements can be controlled, and the precision is not enough, at least they cannot smash molecules or atoms, they can only perform simple arrangements and combinations.

"Hydrogen, oxygen, nitrogen, phosphorus..." Lin En silently thought about the four elements he had manipulated, and he couldn't help but have a few guesses in his heart.

First, the difficulty of element manipulation may be related to the element cycle. For example, official wizards can only manipulate the short-term elements in the first three rows of the periodic table, but cannot control the long-term elements in the fourth to seventh rows.

The second is determined by the number of nuclear charges in the element.

The third is to divide by metal and non-metal elements.

On this point, Lynn once conducted an experiment, trying to use the zero-ring magic [Elementary Material Deconstruction Technique] to disintegrate the steel long sword in his hand.

It turned out that he obviously failed!

No matter how hard Lin En tried, the long sword remained motionless.

This means that with the ability of an apprentice wizard or even a formal wizard, there is no way to directly affect metal elements.

Of course, great wizards and legendary wizards are not necessarily the same.

Because according to the "Basic Principles of Magic", [Elementary Material Deconstruction] also has two advanced magic.

They are four-ring magic [advanced material deconstruction] and seven-ring magic [big disintegration technique]!

Coincidentally, the fourth ring and the seventh ring are the dividing line for being promoted to a great wizard and a legendary wizard!

While Lin En was thinking, he asked 071 to record these contents in the research file, and then turned to the second half of "Basic Principles of Magic". The above descriptions of magic power were even more mysterious.

This legendary wizard regards magic power as the origin of the entire universe, the most basic thing that makes up all matter, and is the real power of creation!

"Is it the source?" Lin En frowned. According to his observations these days, magic seems to exist in every corner of this world, but unlike elements, he can only perceive but cannot really 'see', unless it is Only by using magic like [Magic Missile] can the magic power be materialized for a short time.

Forget it, this is obviously not something he can study clearly at his current level...

Lynn rubbed his aching head, decided to put this question aside first, and then opened the "Detailed Explanation of Elemental Magic".

[Fireball], [Corrosion], [Bright Curse], [Touch of Ice], [Secondary-Hand of the Balrog], [Pyroblast], [Very Poisonous Domain]...

The entire "Elemental Magic Analysis" records a total of seventeen kinds of magic from the first ring to the third ring.

Lin En glanced at those so-called second and third ring magics for a few moments, and then stopped paying attention, but focused on those first ring magics.

With the help of his intellectual brain, although he was able to accomplish magic mimicry as an apprentice wizard, something that only formal wizards could do, he was limited to learning and using one ring of magic.

For example, the principle of the three-ring magic and highly poisonous field is to use magic power to transform into some kind of toxic gas, which may be chlorine or fluorine gas. In short, they are not elements that he can get in a short time.

If he can't analyze it, he can't convert it. His mental power is far from enough to cover such a large area.

In the case of short distances, it is better to simply reduce or increase the oxygen content in the air, which can also achieve similar effects.

With his current ability, learning and improving a ring of magic is the most worry-free.

And one-ring magic also has ordinary and high-level points.

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], strictly speaking, belongs to the upper-level magic of the first level. It is only because of the highly poisonous and indestructible characteristics of white phosphorus that it has reached the level of second-level magic in terms of power.

And another improved magic [White Phosphorus-Balrog's Hand] has a destructive power close to that of the three-ring magic.

But Lynn is well aware of the limitations of white phosphorous fire.

Don't look at him using this thing to kill the Quartet in the Sekas Empire, and even killed An Ruike, who was comparable to the three-ring wizard.

Lin En knew very well in his heart that it was okay to bully those uneducated bishops with this thing, but its power would be greatly reduced if it was used to deal with wizards.

After all, the two important characteristics of White Phosphorus Fire can be dealt with by official 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 hole cards...

(PS: I want everything in the new book! Today, two chapters are released together, and everyone can discuss whether it is better to have more things of this scientific principle nature, or try to be as brief as possible.)

Thanks to the book friend 20200302113752551 for the 1500 starting coins, Xixi Xixi, the momentary smile like a flower 2020 for the 500 starting coins, Mo Yuyang, the 100,000-year-old Tianshan Snow Lotus, and the Local Planning Bureau for the 100 starting coins.