With just two brief sentences, Lynn sent Elock crashing from heaven into hell. The students present all shuddered uncontrollably.
"Olympiad math is an extremely precise discipline. We need to search through vast amounts of exceedingly complex calculations for patterns, then summarize them into corresponding formulas, thereby simplifying the calculations and improving the efficiency of the entire process." Lynn swept his gaze across everyone in the classroom, paused, and spoke again.
"The pattern Elock summarized is not wrong, of course, but its range of application is far too narrow. Since the exponential increase in the squares can be doubled, it can just as easily be tripled, multiplied by five, or multiplied by ten! In that case, this pattern is no longer applicable..."
"And this exponential summation formula applies to every exponential increase that meets the conditions!" Lynn snapped his fingers. As magic surged forth, the complicated formula appeared before them once more.
q ≠ 1, Sn = a1(1 - q^n)/(1 - q)
Joanne, Pierce, and the others stared at the so-called exponential summation formula. After thinking hard for quite some time, they all picked up their quills and began working it out, listing sequences with multipliers of two, three, and four, looking for patterns before trying to substitute them into the formula.
With Elock's earlier summary and the deduction from q ≠ 1, Pierce quickly realized that the symbol likely referred to the multiplier of the increase. But why subtract it from one?
Pierce bit his finger and substituted the original grid game with its doubling growth into the formula. Ignoring the latter part, (1 - q), he calculated directly and found that it worked perfectly—except the resulting number was the exact opposite: negative.
In other words, was the latter part of the formula meant to turn a negative number into