Sample Maple worksheet illustrating series summation and graphing. By Sterl Phinney 2/13/2004.
We wish to expand terms of the geometric series Sum_k=1,n x^k, and compare it to 1/(1-x) for various n:]
> Geomser := (x,n) -> Sum(x^k,k=0..n);
We now compare the two functions for n=7, with the series in blue and 1/(1-x) in red.
> plot([Geomser(x,7),1/(1-x)],x=0..1, y=0..5,linestyle=[1,4],color=[blue,red]);
We now compare the fractional error residuals, making the small values visible by using a logarithmic vertical axis:
Warning, the name changecoords has been redefined
> logplot((1/(1-x) - Geomser(x,7))*(1-x),x=0..1,y=10^(-6)..1,labels=[x,`fractional residual`]);
Now just a warning about plotting points and display resolution:
> plot(sin(53*2*Pi*x),x=0..1,resolution=50,numpoints=50, adaptive=false);
> plot(sin(53*2*Pi*x),x=0..1,resolution=800,numpoints=800, adaptive=false);
Those two preceeding graphs are supposed to be of the same function...! Hope this was helpful.