Induction Proof Calculator

Step-by-step guidance for mathematical induction proofs with automated verification

Proof Type:

Problem Statement:

Induction Variable (typically n):

Base Case Value:

Proof Options:

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Induction Proof Steps

Enter your problem statement and click "Generate Induction Proof" to see the step-by-step solution.

📚 Common Induction Proof Examples

∑

Summation Formula

1 + 2 + ... + n = n(n+1)/2

Inequality

2ⁿ > n² for n ≥ 5

∣

Divisibility

n³ - n is divisible by 6

f(n)

Recurrence

Fₙ = Fₙ₋₁ + Fₙ₋₂ (Fibonacci)

∪∩

Set Theory

De Morgan's Laws

Custom Proof

Enter your own statement

🔍 Mathematical Induction Tips

1️⃣

Base Case

Always verify the base case carefully. It's the foundation of your proof.

2️⃣

Inductive Hypothesis

Clearly state your assumption for n=k. This is your "if" statement.

3️⃣

Inductive Step

Show the statement holds for n=k+1 using your hypothesis.

✏️

Clear Notation

Use consistent notation throughout your proof to avoid confusion.

🔢

Strong Induction

For some problems, you may need to assume all cases up to k.

🧠

Practice

Work through many examples to develop intuition for inductive reasoning.

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Note: This tool provides guidance for constructing mathematical induction proofs. While it can verify algebraic steps, the logical structure and creativity in proofs still require human understanding. Always double-check the generated proofs.