無窮級數示例(2)
Author: 藍邦偉老師

$ 無窮等比級數示例 $

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n = 0 (slider from 0 to 20, step 1)
a = PolyLine((0, 0), (1, 0), (1, 1), (0, 1), (0, 0))
A = Point(a)
B = (0.5, 0.5)
α = Angle((0, 0), B, A)
r: Distance[A, B] / Distance[(0, 0), B]
List = Sequence(Dilate[Rotate[a, α * i, B], r^(i), B], i, 1, n)
k = Element(List, n)
b = PolyLine((0, 0), (1, 0), (1, 1), (0, 1), (0, 0))
List_1 = Sequence((0.1 * k, 0), k, 1, 9)
List_2 = Sequence((0.1 * k, 1), k, 1, 9)
List_3 = Sequence((0, 0.1 * k), k, 1, 9)
List_4 = Sequence((1, 0.1 * k), k, 1, 9)
text1: "$ S=\sum_{k=1}^{\infty}{a_k} $
$\;\;\;=\frac{a_1}{1-r}$
$\;\;=\frac{1}{1-" + (LaTeX[r^(2)]) + "}$
$\;\;=" + (LaTeX[1 / (1 - r^(2))]) + "$"
text2: "$ a_1=1^2=1,r= " + (LaTeX[r^(2)]) + "$"