When q ≠ 1
Sn = a1(1-q^n)/(1-q)
Lynn used magic power as ink to write out the formula represented by the grid game. Then he looked at the apprentices, who had yet to recover from the terror of exponential growth, and spoke loudly.
"Why don't you write this formula down?"
Joanne and the others hurriedly opened their sheets of paper, picked up their quills, and copied down the formula they could not understand at all. The dazed Elock beside them was the best example of what happened when one did not study advanced mathematics!
"Professor Lynn..." Elock looked at Lynn and called out tremblingly. His eyes brimmed with tears, and he was on the verge of crying outright.
"Elock, I heard you say earlier that you were quite good at arithmetic?" Lynn asked.
I'm not, I didn't, don't make things up...
Elock hurriedly shook his head, wanting to deny it, but Lynn waved a hand and continued.
"How about this? If you can accurately calculate the total value of the copper coins in these thirty-six squares before class tomorrow, we'll call off the wager!"
"Of course, you only get one chance to answer!"
Lynn glanced regretfully at the huge pile of coins on the table, though he had no intention of taking them.
First, Elock could not possibly afford that amount. Second, making a group of apprentices empty out their savings over a single game would be a little too frightening.
Who would dare attend his advanced mathematics class afterward?
Elock stared blankly at the floating magical glow. He could not understand what those calculation symbols even were, and he was beginning to doubt whether he could actually do arithmetic at all...
Pierce, who had been envying Elock moments ago, immediately became delighted at his misfortune. Fortunately, he had hesitated.