Geometric Progression Explained — And Why ½ + ¼ + ⅛ + … = 1

Geometric progression in under two minutes. We build from the basics — what makes a sequence geometric (each term × a fixed ratio), the nth-term formula Tₙ = a·rⁿ⁻¹, and the finite sum Sₙ = a(rⁿ−1)/(r−1) — then land on the surprise: when |r| less than 1, you can add infinitely many terms and still get a finite answer. Worked on the sequence 2, 6, 18, 54, … (a = 2, r = 3): T₅ = 162, S₅ = 242. Then a visual proof that 1/2 + 1/4 + 1/8 + … = 1 by tiling a unit square — each new piece fills half of what's left, and the pieces cover the square exactly. Follow @dailymathvisuals for daily visual math. Shop: dailymathvisuals.lemonsqueezy.com #Shorts #math #geometricprogression #infiniteseries #algebra