Mathematical induction

Learn the logic of mathematical induction through precise base cases, induction hypotheses and justified transitions. This optional precalculus proof set covers summation identities, finite geometric sums, divisibility and inequalities, with special attention to the starting index and the difference between evidence and proof.

Single-select and select-all questions progress from recognizing the proof structure to completing algebraic steps and diagnosing invalid arguments. Every explanation identifies what may be assumed, what must be established, and why the conclusion reaches all intended integers. Use the accompanying written-proof prompts for independent reasoning beyond answer recognition.