Xu Ming casually opened his practice book, prepared a draft paper for calculations, and lowered his gaze to the first problem.
"Given a_n = 2n-1 · 3^(n-1), find the sum of the first n terms of a_n, S_n."
If it had been two days ago, he might have been willing but unable.
But now, only the words "full of confidence" remained.
After carefully reading the problem, a solution quickly formed in his mind, and his thoughts were clearer than ever before.
"Is this a problem of summing a sequence where an arithmetic progression is multiplied by a geometric progression? I can use the method of Displacement subtraction ."
While muttering softly, the pen in his hand was already moving.
"S_n = 1 · 3^0 + 3 · 3^1 + 5 · 3^2 + … … + (2_n-1) · 3^(n-1)"
"Multiply by the common ratio q and then subtract with misalignment."
"Simplify…"
"S_n = 1 + (n-1) · 3^n"
From understanding the problem to writing the answer, it only took a little over a minute. Especially when listing the Formula Derivation and simplifying, he didn't even need to think much; it naturally and effortlessly derived itself.
With his confidence greatly boosted, he temporarily suppressed the excitement in his heart and immediately entered into a problem-solving spree.
As time passed by minute by minute, the blank problems in the practice book were solved one by one, and he didn't even stop during the long break between classes.
He only stopped to check the answers when most of the empty spaces were filled.
"They were all correct!" He pulled out the torn-off answer sheet and saw a 100% accuracy rate, his face full of joy.
He had done dozens of problems in these few classes, and such an achievement was indeed something to be proud of.
In addition to the credit for reviewing, the significant improvement in his Formula Derivation ability helped him greatly. It deepened his memory of various formulas and theorems, and crucially, allowed him to apply them flexibly to different types of problems.
This prevented him from merely applying formulas mechanically.
Furthermore, some theorems he had mastered in college also came back to him.
"According to the current situation, as long as I do more problems from now on, I have hope of getting a perfect score in the college entrance exam for mathematics."
Xu Ming pondered to himself, already looking forward to the college entrance exam.
Just as he was envisioning his future, proving conjectures, becoming a great professor, and entering the highest echelons of mathematics, his arm was suddenly bumped by Qian Hong.
"Xu Ming, are you going to the internet cafe this afternoon? We can get two hours on a machine."
Qian Hong turned his head, extending an invitation to team up, and was already starting to clear his desk as he spoke.
Hearing this, Xu Ming glanced at the clock on the back wall and realized it was almost time for lunch dismissal. He was surprised at how quickly time had passed while he was solving problems.
Coming back to his senses, he shook his head and said, "You go ahead, I need to go home."
He couldn't remember the last time he went to an internet cafe, and even now, it held no appeal for him.
Besides, his plans for this afternoon were already set.
After graduating in his previous life, whenever Xu Ming encountered a difficult hurdle, he would recall the warm scenes of living with his parents when he was a child. This would give him motivation and the belief to persevere.
However, the images of his parents in their youth became increasingly blurry, as if they had been deleted from his memory.
To be able to see them with his own eyes again now could be said to be the greatest fortune.
Qian Hong was not surprised by Xu Ming's refusal. He pouted and began to talk about things he encountered at the internet cafe.
"Last time I met a guy from a top high school playing World of Warcraft. He told me how to improve DPS in raids. This time I'm going to try it out and see if it works."
Xu Ming listened to all of Qian Hong's words but was skeptical.
Saying he was playing games, he was probably chatting with his online dating partner. He knew Qian Hong too well when it came to this matter.
Indeed.
Immediately after, he heard Qian Hong say, "Do you need me to log into your QQ for you?"
"No, I don't need it. Just log into your own." Xu Ming smiled knowingly, not exposing his deskmate's true intention.
Speaking of which, his eight-digit QQ number was even applied for by Qian Hong.
Unfortunately, after entering society, people around him gradually stopped using it, so he just left it logged in on his computer every day, treating it as another desktop pet.
Before the bell rang, the first and second-year students from upstairs had already left their classrooms early.
A throng of people came down the stairs, making it much livelier than usual.
In their class, Li Wenhui was sitting at the podium, and only moved his stool back to his seat after the bell rang.
As everyone rushed out, he didn't forget to shout a reminder.
"Roll call at 6:30 PM in the classroom."
However, no one responded.
Xu Ming had his own plans. He didn't go with Qian Hong, and after leaving the classroom, he first went back to the dormitory to get his things.
With a backpack containing dirty clothes, he followed the crowd out of the school gate.
Looking ahead, he could see students in groups of three or five, either going to restaurants to improve their meals or, like Qian Hong, heading straight to nearby internet cafes. Of course, at this time, the main force at internet cafes was still students from other high schools in Dongping County.
After all, most people who could get into Dongping No. 1 High School had a certain minimum level of academic achievement.
They would actively study.
They were not completely degenerate.
Walking on the streets of Dongping County, Xu Ming's eyes darted left and right, recalling the various shops along the way.
During this time, grandpas on tricycles waved at him, but he shook his head and refused them all.
He still insisted on walking.
Finally, after turning two corners and entering a new street, Xu Ming stopped in front of a small handmade wonton shop.
He took a deep breath, his face full of delight.
"It smells so good!"
Before Xu Ming graduated from junior high, he was a typical 'left-behind child,' with both his parents working in big cities to earn money.
On weekends, he would go to his uncle's or aunt's house for meals after returning from school.
The year of his high school entrance exam, he performed exceptionally well and was admitted to Dongping No. 1 High School, becoming the 'child of someone else' that neighbors and relatives talked about. This further strengthened his parents' resolve to return and be by his side, so they rented a house and a shop in Dongping County.
They opened this handmade wonton breakfast shop.
Mainly because Dongping No. 1 High School, as the best high school in the county, was seen by everyone as a stepping stone to a bachelor's degree if one got in.
With a little effort, even a key university was possible.
In contrast, the student quality of the Second High School and Third High School was significantly lower.
As for the somewhat unnoticeable Dongping No. 4 High School, it was called 'Hope High School' by everyone.
Those who know, know.
Unfortunately, after entering Dongping No. 1 High School, he found that his proud academic performance was only considered average in his class.
He suffered quite a blow at the time.
Coupled with his relationship with Zhang Yingxin, he not only failed to get into the key class but also couldn't maintain his scores.
Finally, in order to go to the same school as Zhang Yingxin, he was so foolish as to disregard his parents' objections and choose a more expensive private third-tier university. Every time he thought about it, he felt an urge to hit himself.
Temporarily pushing these chaotic thoughts to the back of his mind, Xu Ming took a deep breath and stepped inside.
Xu Jianguo and Wu Xiulan, wearing aprons, were making wontons. When they caught sight of their son, happy smiles immediately appeared on their faces, and their movements involuntarily quickened.
Xu Jianguo, who was not good at expressing emotions, was the first to speak.
"You're back?"
Although it was only three short words, Xu Ming knew that they contained deep fatherly love.
"Mm."
He had just nodded vigorously in response when his mother's concern already sounded in his ears.
"You haven't had lunch yet, have you?"
"I didn't eat at school. I want to eat the wontons Mom makes." Xu Ming met his mother's gaze, grinning broadly with an honest smile.