Lin En's two short sentences sent Alok from heaven to hell. The students present shuddered.
“Mathematical Olympiad is an extremely sophisticated course. We need to find the patterns in a large amount of extremely complex data calculations, and then summarize them into corresponding formulas to simplify the algorithms and improve the efficiency of the entire calculation.” Lynn looked around at everyone in the classroom, paused, and spoke again.
"Of course the law that Alok summarized is not wrong, but the scope of its application is too small. Since the exponential increase in the square can be 2 times, it can also be 3 times, 5 times, or 10 times! In this way, this law is no longer applicable..."
"And this exponential summation formula is applicable to all exponential increases that meet the conditions!" Lin En snapped his fingers, and under the surge of magic power, the complicated formula appeared in front of everyone again.
When q≠1, Sn=a1(1-q^n)/(1-q) Johnny, Peirce and others stared at the so-called exponential sum formula, pondered for a while, and then picked up their quills to calculate, listing series of two, three, and four times, looking for the rules in them, and then trying to substitute them into this formula.
With Alok's previous conclusion, and through the deduction of q≠1, Peirce quickly realized that this symbol should refer to the multiple of the increase, but why use 1 to subtract? Biting his finger, Peirce substituted the initial 2-fold increase in the square game, and ignored the following (1-q), and directly performed the calculation. He found that it worked completely, but the number obtained was exactly the opposite, a negative number.
Does the following formula convert a negative number into a positive number? However, if we use a 3x exponential growth, the number will be totally wrong...
Peirce's brain was working rapidly. He had already vaguely grasped the answer. Almost, just almost! But what was it?
Throughout the classroom, there were many people like Peirce, concentrating on doing the exercises, some pulling their hair, some scratching their ears, but no one chose to slack off and give up.
Is the learning atmosphere at Yieta Magic Academy so rich? Lin En was somewhat surprised. These people really loved learning...
Most of the class passed quickly, and just when Lin En thought that there would be no results today, a hand was raised high.
"Professor Lynn, I have some ideas!"
It was Johnny who spoke. After receiving the instruction, the girl stood up and said, "In the summation formula, a1 should refer to the number of the first square, q refers to the multiple, and n corresponds to the number of squares, right, professor?"
"That's roughly correct. After class, you can go to the entrance of the academy to collect your reward!" Lynn nodded in response. Although Johnny's statement was very general, it was indeed accurate.
Pierce on the side could not help beating his chest and stamping his feet. After Johnny's reminder, he quickly understood why. It was just a little bit short. He was about to solve it!
After waving his hand for Johnny to sit down, Lynn began to explain to the apprentices present what a geometric sequence is, its general term, and summation formula, and then went on to explain how each formula was deduced.
The wizard apprentices below all picked up their quills very seriously and wrote down every word Lin En said on the paper. Then they tried to change the first term and multiples to verify it repeatedly. The desks were soon filled with various manuscripts...
It has to be said that with the general formula and the summation formula, the speed of calculation is several times faster, and the more complex the formula is, the faster the improvement.
Looking at these students who were more enthusiastic than each other in doing the questions, Lin En couldn't help but sigh that being a professor was too easy! If all the schools in the Federation were like this, why would there be any worry about the development of science and technology?
…
The second Mathematical Olympiad class ended quickly. Alok and the others left the classroom reluctantly, still discussing the derivation of the summation formula...
"About 10%?" The silver-gray-haired girl thought for a moment and replied casually.
"That's a little more than me." The black-haired witch apprentice curled her lips, but there was no envy on her face.
According to rumors, Alok calculated all night without sleep, and when he woke up the next day, he found that the magic power he could control had increased by about 20%. It was this news that set off the entire Yieta Magic Academy.
So this morning, all the wizard apprentices who had no classes came, wanting to hear what kind of magical power this so-called Olympiad math class had, and she was no exception.
The conclusion is also obvious. Complex and tedious mathematical operations can effectively exercise their brain power. The process of logical deduction, finding and cracking numerical patterns is also interesting, at least more interesting than boring meditation.
Johnny ignored the black-haired witch's words and looked back in the direction of the classroom, secretly wondering how many math problems Lin En had solved in the [Secret Law Society] in the past six months to achieve today's achievements...
…
"Doing math problems can actually improve a wizard's control over magic power?"
Of course, Lin En could hear the students' discussion clearly, and was somewhat surprised.
But if you think about it carefully, it seems normal. The reason why his strength increases greatly when he has a mental connection with the intelligent brain is because the overload mode greatly enhances his computing power, or mental power.
This is extremely important for wizards, because the amount of magic power they can control is closely related to the strength of the wizard's own mental power. What makes Lin En feel a little helpless is that this happens to be his blind spot in knowledge.
At least the process of forming a spell position is a bit like practicing an action over and over to form muscle memory.
For example, if you pick up a wine glass from the table and drink it, if it is done by artificial intelligence, it needs to first determine the distance, calculate the angle and strength of holding the glass, and then analyze the most natural arc when picking up the glass and bringing it to your mouth.
Such a complicated process can be completed instantly under the control of the subconscious mind without any hindrance. The same is true for spells. With long-term practice, a single thought can release extremely complex magic.
There is just one prerequisite, that is, the wizard's mental strength is strong enough to provide enough computing power, otherwise the casting process will be prolonged, thus revealing flaws.
Thinking of this, Lin En touched his chin, wondering whether he should give himself a few advanced math problems to calculate...
Maybe it really is useful?
(End of this chapter)