数列の極限

実際に値を計算してみて、極限を推定してみよう。

\sqrt{n^2+n}-n=\frac{(n^2+n)-n^2}{\sqrt{n^2+n}+n}=\frac{n}{\sqrt{n^2+n}+n}

スライダを動かして、数列の値を確認し、その極限を推定してみよう。

A = Point(yAxis)
B = (2, 1)
C = Point(yAxis)
D = (2, -1)
b = Line(C, D)
E = Point(yAxis)
F = (2, 0.5)
c = Line(E, F)
G = Point(yAxis)
H = (2, -0.5)
d = Line(G, H)
n = 1 (slider from 1 to 30, step 1)
I: (n, sqrt((n * n) + n) - n)
e: y(I)
テキスト1: "\sqrt{n^2+n}-n=\sqrt{" + (LaTeX[n]) + "^2+" + (LaTeX[n]) + "}-" + (LaTeX[n]) + "=" + (LaTeX[e]) + ""
f: sqrt(n^(2) + n) + n
テキスト2: "=\frac{" + (LaTeX[n]) + "}{\sqrt{" + (LaTeX[n]) + "^2+" + (LaTeX[n]) + "}+" + (LaTeX[n]) + "}=\frac{" + (LaTeX[n]) + "}{" + (LaTeX[f]) + "}=" + (LaTeX[e]) + ""