Taylor series: Error estimation

Trying to estimate the error for taylor series expansion for 1/1-x. I'm trying to see the convergence for various values of N (no. of iterations) within a certain domain (x). I want to know how to calculate the error and plot it vs changing N.

This is what I have so far:

x= -0.9:0.05:0.9;

y= 1./(1-x);

N = 1; %N: no. of terms

y1 = 0*y;

for i = 0:N

y1= y1+(x.^i);

e1= abs(y-y1);

end

N2 = 2;

y2=0*y;

for i = 0:N2

y2 = y2+(x.^i);

e2= abs(y-y2);

end

N3 = 10;

y3=0*y;

for i= 0:N3

y3= y3+(x.^i);

e3= abs(y-y3);

end

N4 = 100;

y4=0*y;

e4 = 0*0;

for i = 0:N4

y4 = y4+(x.^i);

e4 = abs(y-y4);

end

hold on

plot(x,y,'*r')

plot(x,y1,'-b');

plot(x,y2,'^g');

plot(x,y3,'>k');

plot(x,y4,'--m');

hold off

figure

hold on

grid on

plot(1:N+1,e1,'ok'); %Matlab shows an error while doing this

plot(1:N2+1,e2,'-b');

plot(1:N3+1,e3,'^g');

plot(1:N4+1,e4,'pc');

hold off

Answer 1

[David Hill]

x= (-0.9:0.05:0.9)';
y= 1./(1-x);
m=cumsum(repmat(x,1,101).^(0:100),2);
err=abs(y-m);
surf(repmat(x,1,101),repmat([0:100],37,1),err);
figure;
hold on;
grid on;
plot(x,y,'*r');
plot(x,m(:,2),'-b');
plot(x,m(:,3),'^g');
plot(x,m(:,11),'>k');
plot(x,m(:,101),'--m');

[Rahul Janardhanan]

Can you please elaborate about what the surf plot displays? Thanks!

[David Hill]

The surface plot is displaying all the x-values, N from 0-100, and corresponding errors on the z-axis.