function []=hw4_2_4(a,b,n)

% makes an nxn Triadiagonal matrix with a's on the main diagonal 
% and b's above and below, and test the convergence of the geometric series
% for different values of a and b

% first make an n-long vector of all a's and an (n-1)-long vector of all b's
u=a*ones(1,n);
v=b*ones(1,n-1);

% now use the command diag to put these vectors on the appropriate diagonals of
% a matrix A
A=diag(v,-1)+diag(u)+diag(v,1);

% add up 5 and 10 terms of the series
GS5=zeros(n);
for k=0:5
    GS5=GS5+A^k;
end
GS10=GS5;
for k=6:10
    GS10=GS10+A^k;
end

% compare the partial sum to the result of the geoemetric series theorem
GS=inv(eye(n)-A);
disp('error after 5 terms')
disp(norm(GS-GS5))
disp('error after 10 terms')
disp(norm(GS-GS10))