Binomial theorem, Pascal's triangle, and proof by induction

MathematicsAlgebraAges 15–16

The expansion of (a + b)ⁿ has coefficients equal to row n of Pascal's triangle. Increase n step by step to see how each new row is generated from the previous one via the identity Cₙᵏ⁻¹ + Cₙᵏ = Cₙ₊₁ᵏ – exactly the induction step P(n) ⇒ P(n + 1) – alongside a falling-domino chain illustrating the principle of induction, the general term, the coefficient sum 2ⁿ, and the largest term once a and b are set to numbers.