Animated convergence of a series of functions
This applet displays the animated convergence of a series of functions by displaying
first
n partial sums.
Some examples:
- geometric series:
f(x)=1/(1-x), g0(x)=1, gn(x)=x^n,
ili
f(x)=1/(1-x), gn(x)=x^(n-1)
(n always starts at 1)
- power series:
gn=1/(1-x^2)
- Taylor (MacLaurin) series:
f(x)=sin(x), gn(x)=x^(2*n-1)*(-1)^(n-1)/(2*n-1)!
- Fourier series:
f(x)=abs(sin(2*x))-sin(2*x),
g0(x)=2/pi-sin(2*x),
gn(x)=4/pi*cos(4*n*x)/(1-4*n^2).
You can zoom on the interesting details by clicking the detail with the mouse.
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