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Mathematical Induction Calculator

Online induction verifier: using 1+…+n=n(n+1)/2, confirm both sides for a given n and see the base + inductive structure.

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Base step + inductive step
Positive integer

📖 Tutorial | Induction

1. Definition
Induction proves integer statements: ①base step at n=1; ②inductive step assuming n=k, prove k+1; then all positive integers.
2. Formula & Notation
nNumber of terms
3. Properties & Laws
  • Both steps are required;
  • The hypothesis underpins k+1;
  • Truth propagates like dominoes;
  • Here 1+…+n=n(n+1)/2.
4. Steps
  1. Enter n;
  2. Click "Verify" to compare sides;
  3. Or click "Load Example".
5. Worked Examples
Example: n=10: LHS=55, RHS=10·11/2=55.
6. Common Pitfalls
Prove the base step first;
The step must use the hypothesis;
Finite checks are not a proof.

❓ FAQ | Induction

Two steps?
Base, inductive.
Why works?
Truth propagates.
Hypothesis?
Assume n=k.
Other start?
Begin at n₀.
Uses?
Identities, inequalities, divisibility.
n=10 enough?
No.
RHS here?
n(n+1)/2.