Eulers Number Code and Questions

My current code follows, but is in error when I enter "1" as the input. DO you see the problem?:

function [est k ] = approximate_e( delta )
%APPROXIMATE_E Summary of this function goes here
%   Detailed explanation goes here
n =1;
est = 0;
while abs(exp(1)-est)>delta 
    if n ==1
        est = 1;
    end
    if n == 2
        est = 2;
    end
    if n >2
        est = est+1/prod(1:(n-1));
    end
    fprintf "e is %d and n is %d:  \n",est,n
    k = n;
    n = n + 1;
    if n >10000
        fprinf "n is greater than 10000.\n"
        break;
    end
end

I'm trying to solve for the problem statement below:

Write a function called approximate_e that uses the following formula to compute e, Euler’s number:

Instead of going to infinity, the function stops at the smallest k for which the approximation differs from exp(1) (i.e., the value returned MATLAB’s built-in function) by no more than the positive scalar, delta, which is the only input argument. The first output of the function is the approximate value of e, while the second is k. (Note: if your program or the grader takes a long time, you may have created an infinite loop and need to hit Ctrl-C on your keyboard.) You are not allowed to use the built-in function factorial.

Answer 1

[DJ V]

Okay, solved it.

[Ramon Cajal]

I am struggling with this one. I'd appreciate understanding how did you get it right My code looks like:

 function [e,k] = approximate_e( delta )
k= 0;
e = 0;
Bailout = 10000;
while abs(exp(1)-e) >delta 
    e =e+(1+(1/prod(1:k)));
    k = k + 1;

    if k > Bailout
        break;
    end
end

Answer 2

[JESUS DAVID ARIZA ROYETH]

You Can use this:

function [est,n ] = approximate_e( delta )
  n=-1;
  est=0;
  while abs(exp(1)-est)>delta 
      n=n+1;
      est=est+1/factorial(n);
  end

Answer 3

[DJ V]

Can't use factorial.