"For the sum of the first N terms, everything in the middle cancels out, leaving only 1/S_0 - 1/S_N."
"Because ∑ a_n diverges, S_n approaches infinity, so 1/S_n approaches 0."
"Therefore, the series converges."
Li Dong put down his pen.
The air in the room suddenly fell silent.
Lu Yao stared blankly at the scratch paper.
She had spent half an hour on it last night, trying all sorts of complicated ratio tests, and yet...
When Lu Yao didn’t say anything for a long moment, Li Dong thought he had made a mistake and asked nervously.
"Senior? Is it wrong? I noticed the structure looked a lot like the partial fraction decomposition we learned in our first year of high school, so I just gave it a try..."
Lu Yao snapped back to her senses and began to mutter to herself.
"Squeezing... partial fractions... That works too?"
"It really does converge... The answer is correct..."
She looked up, staring at Li Dong with a resentful gaze.
Li Dong was a little flustered by her stare, thinking to himself.
’Why is she looking at me like that?’
’How come her expression looks just like Misha’s? It’s like she wants to eat me alive.’
’Are all pretty girls this weird?’
Finally, Lu Yao stammered.
"How... How did you think of splitting the denominator into the product of two terms and then using the squeeze method? That’s... That’s a very advanced technique!"
Li Dong scratched his head.
"Didn’t you just say I needed to learn how to ’construct’ things? I was just thinking about how to get rid of the squared term, so I tried it."
Lu Yao felt like she had just taken 10,000 points of critical damage.
Over the next while, the dynamic slowly started to get a little weird.
Lu Yao: "What about this problem, then? What if it’s an alternating series?"
Li Dong: "Oh, for that one, you can just use the Leibniz test. See, it’s monotonically decreasing and approaches zero..."
Lu Yao: "And changing the order of integration for this double integral?"
Li Dong: "Just draw a graph and it becomes clear. Integrate with respect to y first, then x..."
Lu Yao nodded furiously beside him, her pen scribbling notes nonstop, completely forgetting that she was the one getting paid to be the tutor.
GRUMBLE...
An ill-timed sound shattered the academic atmosphere.
A blush flashed across Lu Yao’s face, and her pen stopped moving.
Li Dong glanced at the time and realized it was already past one in the afternoon.
"Uh... Sorry, Senior. I lose track of time when I’m doing problems."
Li Dong smiled apologetically.
"My mom’s not home. I usually just make instant noodles for lunch. If you don’t mind..."
Lu Yao glanced at Li Dong.
Her dignity as a third-year university senior was already in pieces on the floor.
’My math skills aren’t up to par, but I must be better at cooking than this junior, right?’
"Instant noodles? There’s no nutrition in that."
Lu Yao stood up and rolled up her sleeves.
"I’ll cook! Let me show you what your Senior is capable of!"
This was a pleasant surprise for Li Dong.
"You can cook?"
Li Dong looked at Lu Yao, a trace of admiration flashing in his eyes.
"University students really are different! Not only are you good at solving problems, but you can cook too!"
"When I get to university, does that mean I’ll learn how to cook?"
If a certain university president knew that Li Dong’s aspiration for higher education was based on the idea that "they teach you how to cook in university," he’d probably get angry enough to elbow-drop the Earth on the spot.
"Of course!"
Lu Yao walked into the kitchen, brimming with confidence.
Five minutes later, however, the kitchen was filled with smoke. Lu Yao stood there with a spatula in one hand and her phone in the other, the screen clearly displaying a video titled "Homestyle Scrambled Eggs with Tomato."
"Do the eggs go in first, or the tomatoes? Ah! The oil is splattering!"
Li Dong: "..."
He asked cautiously.
"Senior Sister Lu, when you said you could cook... did you mean you’re learning from a phone tutorial right now?"
Lu Yao slammed the kitchen door shut with a BANG.
"None of your business! Just wait outside!"
Half an hour later, two bowls of rice were set on the dining table, with a plate of strangely colored scrambled eggs and tomato in the middle.
Li Dong picked up a piece of blackened egg with his chopsticks, hesitating.
"Senior Lu, you spent an hour slaving away in the kitchen... for this... charcoal-grilled scrambled eggs with tomato?"
Lu Yao shot him a glare, then shoveled a mouthful of rice into her own mouth and mumbled indistinctly.
"Eat it or don’t!"
They both ate the meal in an exceptionally awkward silence.
After the meal, Lu Yao couldn’t stand to stay a moment longer.
The blows she had suffered today were simply too great.
Besides, her mind was a jumble from all the concepts Li Dong had just explained to her, especially that "partial fraction-squeeze" method. She needed to go back and properly digest and solidify her understanding.
"Um... I’m going to head out. You should get some rest too."
Lu Yao grabbed her bag, ready to flee.
"Wait a second!"
Li Dong suddenly called out to her.
Li Dong ran back to his bedroom and returned a moment later with two red banknotes.
"Senior Lu, my mom left this for you. She told me to give it to you directly."
Li Dong handed over the money.
"Last time was one hour, this time was about two, so that’s 150 yuan total. And you even made me a meal, so let’s make it 200. Keep the change."
Li Dong was so focused on completing the task his mother had given him that he didn’t notice the incredible expression on Lu Yao’s face.
Lu Yao stared at the bright red banknotes, her face burning with shame.
’This 150 yuan... is he mocking me?’
’He was the one explaining the problems to *me* today, wasn’t he?’
’And now he’s paying *me*?’
Lu Yao glanced up at Li Dong and saw that the boy’s eyes were perfectly clear, completely devoid of any mockery.
"Huuu..."
Lu Yao took a deep breath and pushed Li Dong’s hand away.
"No, thank you!"
"Keep the money and buy some books for yourself!"
With that, she bolted out the door as if escaping.
Before the door closed, she turned and shouted, "I’ll be back next week!"
"Okay!" Li Dong readily agreed.
Staring at the closed door, Li Dong was in a great mood.
For him, today’s tutoring session had been a massive gain.
The concepts from *Mathematical Analysis* and *Advanced Algebra* that he had once brute-forced his way through were finally brought to life by the stream of problems Senior Sister Lu had fed him.
’University students really are something else,’ he thought.
He recalled Lu Yao’s expression just now—angry, yet still earnestly explaining things—and that plate of scrambled eggs with tomato, which was not just bad, but truly, exceptionally bad.
The corners of Li Dong’s mouth turned up slightly.
’Even though Senior Sister Lu stares at me for no reason, just like Misha.’
’I think I prefer Senior Sister Lu’s type.’
’After all, she’s a bit older, knows more, and her knowledge is more systematic...’
Monday was not going to be a good day for most students at Jiangcheng Seventh Middle School.
It was the day of the monthly exams.
In the classrooms, the underachieving students were sighing and groaning, each looking as if they were being led to their execution.
But some people were unusually excited.
For the past month, Jiang Yizhou had hired a private tutor, ground through countless practice tests, and even uninstalled *Honor of Kings*.
And for what?
It was all to crush that suddenly prominent Li Dong under his heel in this month’s exams!
However, right up until the bell rang for the first exam, Language Arts, the seat in the back row by the window remained empty.
Li Dong hadn’t come to school today.
The feeling of punching a fistful of cotton made Jiang Yizhou extremely uncomfortable.
’Hmph, avoiding me at my sharpest?’
From the front row, Misha also glanced back at the empty seat.
A trace of disappointment flashed in her eyes.
’360 points? Is that for real?’
「At this very moment.」
In a computer lab in one of the academic buildings.
Li Dong was sitting in front of a computer, the screen displaying:
[The 16th Annual "Huaxuan Cup" National Physics Innovation Competition (Preliminary Round)]
[Examinee: Li Dong]
[Begin Exam]

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