Question

11. (10 points) - MATLAB ce of the alternating harmonic series, shown below: 1-2?--+ - 3 4 5 Use a loop to determine when the series has converged within a tolerance of 0.001. The animation should show how the value of the series changes as each successive term is added, resulting in a final

Answer 1

Matlab Code:

clc;
clear;
sum=0;    %sum of series
i=1;      %iteration variable
er=1;    %error

% making animation and seting axes
curve=animatedline;
set(gca,'XLim',[0 1000],'Color',[.7 0.9 0.9]);
title('harmonic Series Animation','FontSize', 20);
xlabel('count','FontSize', 16); ylabel('Sum of Series','FontSize', 16);
while er>0.001
    nsum=sum+(-1)^(i+1)*1/i;
    S(i)=nsum;
    C(i)=i;
    addpoints(curve,C(i),S(i));
    drawnow
    i=i+1;
    er=abs(nsum-sum);
    sum=nsum;
end

Sample Output:

Run the above code ,

Below figure will be obtained at end of animation ..

harmonic Series Animation 0.95 0.9 0.85 0.8 0.75 CO 0.7 0,65 0.6 0.55 0.5 100 200 300 500 600 700 800 900 1000 count

Zoomed image:

harmonic Series Animation 0.85 0.8 0.75 O 0.7 0.65 0.6 10 20 40 50 60 count

Please comment if any doubt is there.. i will help. (y)