Examples for

Step-by-Step Proofs

Mathematical Induction

Prove a sum or product identity using induction step by step:

Prove divisibility by induction:

Derive a proof by induction of various inequalities step by step:

Prove a sum identity involving the binomial coefficient using induction:

Approximate the bounds of harmonic numbers using induction:

Series Convergence

Show how to prove if a sum of infinite terms diverges or converges with different tests: limit test, ratio test, root test, integral test, p-series test or geometric series test.

Investigate the convergence or divergence of an infinite sum step by step:

Trigonometric Identities

See the steps toward proving a trigonometric identity:

Prove equalities between tangent, sine and cosine:

Show the proof for equalities between trigonometric functions like tangent, arctangent, cosecant and secant:


  • Trigonometry
  • Go Pro NowLearn more about Wolfram|Alpha Pro »