% Computes e using the Taylor's series for e^x
% Inputs:   N - the number of terms + 1 that is summed in the series.
% Outputs:  e - an approximation of e
function e = compute_e(n)

% Initialize the variable used for the partial sums.
e = 0;

% This is the slow way to implement the sum in MATLAB.
for j = 0:n
   % Note that MATLAB has no built in function for factorial, so we use the
   % result that gamma(n+1) = n!.
   e = e + 1/gamma(j+1);
end

% The fast way to implement the sum is as follows (note: just uncomment out
% the following two lines.
% k = 0:n;
% e = sum(1./(gamma(k+1)));