Infinite Geometric Series Visualization A geometric proof that 1/3 = ∑_{i=1}^∞ 1/4^i = 1/4 + 1/4² + 1/4³ + 1/4⁴ + 1/4⁵ + ⋯ The shaded triangles inside the large triangle represent the successive terms of the series; their areas sum to exactly one-third the area of the large triangle.