數列的極限示例
Author: 藍邦偉  老師

$ O $

$ 數列的極限示例 $

$a_n=\frac{2n}{n+1} $

$ b_n=\frac{5}{2^n} $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.8 * Corner[1] + 0.2 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
ex = 0 (slider from 0 to 2, step 1)
List_1 = Sequence((k, 2 * k / (k + 1)), k, 1, 100)
zoom = 1 (slider from 0.1 to 1, step 0.1)
n = 1 (slider from 1 to floor(x(Corner[2])), step 1)
q = GCD(n + 1, 2 * n)
text2: "$ a_{" + (LaTeX[n]) + "}=\frac{" + (LaTeX[2 * n]) + "}{" + (LaTeX[n + 1]) + "} " + (LaTeX[If[q ≠ 1, "=" * FractionText[2 * n / (n + 1)], ""]]) + "$"
P_1: (n, 2 * n / (n + 1))
List_2 = Sequence((k, 5 / 2^(k)), k, 1, 100)
P_2: (n, 5 / 2^(n))
text4: "$ b_n=\frac{5}{2^{" + (LaTeX[n]) + "}} =\frac{5}{" + (LaTeX[2^(n)]) + "}$"