% m-file contains an example of useful functions using % Compute 5! n = 10; prod(1:n); % compute sum of ten first numbers sum(1:n) % compute the vector containing subsequent products of its elements cumprod(1:n) % compute the vector containing subsequrent sums of its elements cumsum(1:n) % compute value of sinus(k) (from its definition!) % x - x^3/3! + x^5/5! + ... + (-1)^n x^(2n + 1)/ (2n + 1)! % a bit of math: what kind of power series is it? % odd powers so we need construct a vactor of odd values % n from the definition n = 10; n1 = 2*[0:n] + 1; % compute vector of (2n + 1)! t = cumprod(1:(2*n + 1)); % compute vector of 1/(2n+1)! r = 1./t(1:2:end); % point of computation k = 2; % k to different powers defined by p p = k.^n1 % how about signs? s = (-1).^[2:(n+2)] % and together output = cumsum(s.*p.*r) % exact value output2 = sin(k) % to plot % How do you describe the convergence of the "output" series? plot([0:n], output, 'ro', [0:n], output2*ones(1, n+1), 'b-'); title(['Sinus for k = ', num2str(k)]); xlabel('n'); ylabel(['sin(', num2str(k), ')']); % as it is seen from the example above the prod, sum, cumsum and cumprod functions can be successfully applied to power expressions