尤拉數e
Author: 藍邦偉  老師

拉動m或n觀察極限值

ℯ≈ \frac{ 1 }{ 0!} 

+ \frac{ 1 }{1! } 

+ \frac{ 1 }{ 2!} 

=1

=2

=2.5

+ \frac{ 1 }{3! } 

+ \frac{ 1 }{ 4!} 

+ \frac{ 1 }{ 5!} 

+ \frac{ 1 }{ 6!} 

+ \frac{ 1 }{7! } 

+ \frac{ 1 }{ 8!} 

+ \frac{ 1 }{ 9!} 

+ \frac{ 1 }{10! } 

+ \frac{ 1 }{ 11!} 

+ \frac{ 1 }{12! } 

+ \frac{ 1 }{14! } 

+ \frac{ 1 }{ 13!} 

 +\frac{ 1 }{ 15!} +...=2.71828

=2.66667

=2.70833

=2.71667

=2.71806

=2.71825

=2.71828

=2.71828

=2.71828

=2.71828

=2.71828

=2.71828

=2.71828

$ 考慮(1+\frac{1}{n})^n\; ，\;當n→∞時\;，\;這個值就是e $

$  Euler\;\; e$

Reset

f(x) = 2 * sin(x) + cos(2 * x) + 2
n = 1 (slider from 1 to 10000000, step 1)
m = 1 (slider from 1 to 16, step 1)
A = (-0.28, 1.98)
B = (-0.68, 1.42)
a: y = y(B)
text2: "$ (1+\frac{1}{" + (LaTeX[n]) + "}) ^{" + (LaTeX[n]) + "}=" + (LaTeX[(1 + 1 / n)^(n)]) + "$"