I was hoping somebody would be able to help me as I am pretty new to Matlab. I am trying to create a for-loop to describe the taylor series expansion of cos(x)= (-1)^n*x^2n/(2n)! and to see how it converges towards cos(x). Below is the code that I have used to plot the different orders of n, but I was wondering if there was a way to make this work for any value of n? n=0; for x = -6:0.25:6 n=n+1; y(n)=x; F(n)=cos(x); F0(n)=1; F2(n)=1-0.5*x^2; F4(n)=1-0.5*x^2+(1/24)*x^4; end plot(y,F,y,F0,y,F2,y,F4) axis([-6 6 -1.5 1.5]) I have tried n=0; for x=(-2:.25:2) n=n+1; Y(n)=x; F(n)=cos(x); G(n)=1+(-1)^n*x^(2*n)/prod(1:2*n); end plot(y,G) but the plot for G does not come close to cos(x) as the values of n are not constant and the plot goes to zero. Any help would be greatly appreciated.