Can anyone find the error in my code?

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.

 function [e, k] = approximate_e( delta )
k= 0;
e = 0;
while ((exp(1))-e) > delta 
    k = k + 1;
    e = e + 1/prod(1:k);
    if k > 1000
        break;
    end
end

note: this code fails to produce the correct output for delta = 1

YOU CAN'T USE THE FACTORIAL FUNCTION

[Akira Agata]

Let me clarify.

Using the Taylor expansion, exp(1) can be expanded as follows:

 exp(1) = 1 + (1/1) + (1/2!) + (1/3!) + ...

On the other hand, your code calculates following equation.

 (1/1) + (1/2!) + (1/3!) + ...

So, I think the code correctly generates ~1.718.

[Steven Liu]

e should be 1, not 0. Problem solved!

Answer 1

[Srishti Saha]

Hey, this piece of code works just fine:

%function to compute euler's number
function [approx_e, k] = approximate_e (delta)
% Set the variables for the while loop.
 k = 0;
 fact = 1;
 approx_e=1;
 while abs(approx_e - exp(1)) > delta

       k=k+1;

       fact = fact * (1/k);
       approx_e = approx_e + fact; 
   end
   approx_e;
   k;
end