Write a function called approximate_e that uses the following formula to compute e, Euler’s number: = 1 ! ∞ = 1+1+ 1 2 + 1 6 + 1 24 +⋯ Instead of going to infinity, the function stops at the smallest k for which the approximation differs from

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function [est, n ] = approximate_e( delta )
%APPROXIMATE_E Summary of this function goes here
% Detailed explanation goes here
n =1;
est = 0;
while abs(exp(1)> delta
if n ==1
est = 1;
end
if n == 2
est = 2;
end
if n >2
est = est+1/prod(1:(n-1));
end
n = n + 1;
if n >10000
break;
end
end
could you please tell me how one can solve above mention question. thanks
  14 Comments
Jorge Briceño
Jorge Briceño on 4 Feb 2018
Hi everyone,
Why do not you try this? I explained what the variables are doing.
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
% The counter k is necesary for factorial calculus. If you put it after
% the approx_e, it will add an addional number since the condition will be
% reevaluated.
k=k+1;
% For factorial calculus one could use:
% fact = fact * (1/k) or prod([1 : n])
% fact and approx_e is calculated to recursive method.
fact = fact * (1/k);
approx_e = approx_e + fact;
end
approx_e;
k;
end
I think you should also review the if statements, since you could try using if-elseif statements, in other to make your code a bit more readable. Also, try to add notes (ctrl R) so you will make yourself aware of what you are coding.

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Accepted Answer

James Tursa
James Tursa on 19 May 2017
You need to change your while loop criteria to compare your estimate with exp(1). E.g.,
while abs(est-exp(1)) > delta
  16 Comments
Jan
Jan on 28 May 2017
@Wasi: Then restore the former version from your backup. Do you know how to use the "Fromer versions" provided since Windows 7?
If you cannot m,anage to restore the correct version, post the current code and explain, what does not work as expected.

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More Answers (4)

Srishti Saha
Srishti Saha on 1 May 2018
Tested this:
%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

Jan
Jan on 28 May 2017
Edited: Jan on 28 May 2017
function [est, k] = approximate_e(delta)
k = 0; % Start with 0'th iteration
est = 0;
want = exp(1); % Do not calculate this repeatedly
Fac = 1;
while abs(est - want) > delta && k < 10000
k = k + 1; % *Before* appending the new term!
if k <= 2
est = est + 1;
else
Fac = Fac * (k - 1); % Cheaper than PROD()
est = est + 1 / Fac;
end
end
  9 Comments
Jan
Jan on 13 May 2018
@Ranil: "Error using input Cannot call INPUT from EVALC." - My code does not contain an input command. So what do you call "your code" exactly? The message is clear: Use an input argument for the function, not an input() command.

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rishabh gupta
rishabh gupta on 4 Feb 2018
Edited: Walter Roberson on 13 May 2018
This could also be done without using if condition, and it works too...
function [ app_e , k ] = approximate_e( delta )
app_e = 1;
k=0;
facto=1;
exp_1 = exp(1);
while abs(app_e - exp_1) > delta
k=k+1;
facto = facto*k;
app_e = app_e + 1/facto;
end
app_e = app_e;
k
end

Ranil Fernando
Ranil Fernando on 13 May 2018
Edited: Ranil Fernando on 13 May 2018
I'm getting the bellow error for my code when using the grader; Any one hen help me with why, many thanks. But the code works just fine when using without the grader.
Problem 4 (approximate_e): Error using input Cannot call INPUT from EVALC.
Error in factorial (line 7) n=input('Specify a integer to calculate factorial : ');
Error in hw6
Error in hw6
Error in hw6
Error in hw6
Error in hw6.
______________________________________________________________________________
And the code is;
function [app_e,k] = approximate_e(delta)
sum = 0;
app_e = sum;
k = 0;
fact = 0;
while (exp(1)-app_e) > delta
if k==0 || k==1
fact=1;
else
fact = fact*k;
end
k = k + 1;
sum = sum + 1/fact;
app_e = sum;
end
end
  2 Comments
Ranil Fernando
Ranil Fernando on 13 May 2018
This really helps, Thanks a lot @Walter. Thanks for the advice on not to make a variable with a name sum. I've made the correction. Many thanks.

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