How do I run an infinite series by creating a function?

I am working on a homework problem and cannot seen to get it started properly. So far I have a function created,

if true
  % function [e]=Euler(x,n)
    e=1/factorial(x);
    for k=0:n
       e=e+(1/factorial(k));
    end
    end
end

I just seem to have hit a wall now and cannot get passed it. I am trying to use the infinite series for Euler's number:

And I need to calculate and then stop within 1e-7.

Answer 1

[Star Strider]

You’re missing a test for convergence. I don’t understand your needing any arguments for your function, since it never uses them. It calculates the series and is entirely self-contained. I would just set ‘n’ arbitrarily high and break out of the loop when it converged.

n = 150;
e=0;
ep = 0;                     % Previous Value Of ‘e’
for k=0:n
    e=e+(1/factorial(k));
    if e-ep < 1E-7          % Test For Convergence
        break
    end
    de = e;
end

When I ran it, it required only 11 iterations to converge. (I would use a while loop, but your code works with a high enough value for ‘n’.)