Mathematica(@mathemetica):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.

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Mathematica@mathemetica

2026.05.19 12:14

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.