Proof Without Words: Sum of First n Cubes
2012-10-09 04:54
This GeoGebra applet provides a visual proof without words for the sum of the first n cubes formula. Using sequence and mirror commands, it constructs geometric shapes and rectangles to demonstrate area relationships dynamically, helping learners understand the algebraic identity through visual geometry.
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<input a0="Sequence[(i, j), i, 0, ((n * (n + 1))) / 2 - 1]" a1="j" a2="0" a3="((n * (n + 1))) / 2 - 1"/>
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<input a0="Sequence[Polygon[((2 * f(i)^(2)) + f(i) - 0.5, ((j - 1) * ((2 * f(i)) + 1)) - 0.5), ((2 * f(i)^(2)) + (3 * f(i)) + 0.5, ((j - 1) * ((2 * f(i)) + 1)) - 0.5), 4], j, 1, f(i)]" a1="i" a2="1" a3="n"/>
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