Owl: A sequence is just an ordered list of numbers — a₁, a₂, a₃, … — indexed by the positive integers. Think of successive snapshots of a fading echo, or daily readings on a sensor as it cools toward room temperature.
Convergence means those snapshots approach a single number L. Divergence means they don't: they wander, oscillate, or escape to infinity.
Before any algebra, picture aₙ = 1/n. Where is that heading? And is "bounded" the same as "converges"?
We'll plot terms, practice limit tricks, and meet the monotone-and-bounded guarantee — plus a trap about recursive updates that never settle.