A base. A bridge.
Every integer.
Explore mathematical induction by comparing an arithmetic sum with a proposed formula. Inspect the exact starting case and the algebra that must carry every case to the next.
Works offline · exact arithmeticChoosing an example checks it immediately. Change any coefficient to make your own conjecture, then check it explicitly.
2. Check the base
The actual base is computed from the terms. An empty sum has value 0, with no extra k = 0 term.
3. Derive the successor
For an arbitrary allowed n, assume S(n) = Q(n). Then S(n + 1) = Q(n) + t(n + 1). We must show that this equals Q(n + 1).
4. Check the identity for every n
This lab checks only arithmetic sequences and quadratic rational conjectures. It supplies the displayed algebra for that family; it does not decide arbitrary mathematical statements.
Inspect one successor substitution
Finite examples are illustrations
Matching several rows alone is not an induction proof. One different row does refute equality at every integer in the stated domain.
| n | Actual S(n) | Proposed Q(n) | Comparison |
|---|
Keep learning
The twelve-question lesson covers base cases, successor algebra, missing bridges and the limits of finite checks. Save its JSON, open the RecallWeave learner, choose the file, review its preview and start the lesson.
Open the sibling RecallWeave learner when the project folder is present. Downloads are explicit; no learning session or browser storage is changed.