How can I sum a number of terms as a polynomial?

My code performs the individual calculation of each term of my polynomial, which is not exactly a polynomial, however, I need it to output the total sum of all these terms, I have no idea what to do. In my code x is the input, I have been using 1 to facilitate the calculations, and n is the number of terms that must be added to my final result:

while i<=n
    
    ex = (x^i);
    fat = factorial(i-1);
    soma = ex / fat; 
    i=i+1;

Answer 1

[dpb]

"Dead ahead" straightforward would be

S=0;
for i=1:n
  S=S+x^i/factorial(i-1);
end

Alternatively, vectorized could be

i=1:n;
S=sum(x.^i./factorial(i-1));

[Gabriel]

but that doesn't solve my problem, I need the total sum of the results of my variable "soma"

[John D'Errico]

@Gabriel

Why do you think it does not form the sum? Read the answer again.

[Gabriel]

cause it loops.

the full code is:

%Polinomio de Taylor
x = input("Entre com x: ");
n = input("Entre com n inteiro positivo: ");
i=1;
if n <= 0
    fprintf('Valor invalido , entre com um valor inteiro e positivo para n. '); 
    n = input("Entre novamente com n inteiro positivo: ");
    
else
    
    funcao = x*exp(x);
    
    while i<=n
        
        ex = (x^i);
        fat = factorial(i-1);
        soma = ex / fat; 
        i=i+1;
    end 
end

if you enter x = 1 and n = 5 it will generate 5 terms, which I need to add the 5 terms to get my final result, which would be approximately 2.71, for this example

[Bruno Luong]

"would be approximately 2.71, for this example"

You want then to approximate e = exp(1) in that case your loop is wrong (the power and the factorial)

dpb ust duplicates your mistake, don't blame him.

[Gabriel]

don't get me wrong, i didn't blame anyone, the result approximates e = exp(1), because it is based on a taylor series, which has x*e^x as target function, and since the input value of x was = 1, the result is close to this. if you notice, the idea is to find a sum of n terms to approximate the target function.

[dpb]

You didn't tell us the end objective, just asked how to sum the terms you had defined.

[Gabriel]

you are right, my bad. could you help me please?

[Torsten]

Initialize soma to 0 and use soma = soma + ex/fat, not soma = ex/fat which is incorrect.

I don't understand why you don't adapt your code to what @dpb gave you.

[Bruno Luong]

So OK dpb code works fine. Why do you says "that doesn't solve my problem"

x = 1;
n = 5;
S=0;
for i=1:n
    S=S+x^i/factorial(i-1);
end
S

S = 2.7083

Pretty close to 2.71 as you expect. Do you want soma instead of S, or because 2.7083 is not 2.71?

[Gabriel]

@Bruno Luong the code worked, and I understood what was wrong, thank you very much. I started to learn matlab a little while ago, it really helped me a lot, would it be possible to stop the run automatically when this result was displayed?

[Bruno Luong]

You have to estimate the error using Taylor remainder estimation first formula here during the loop and when the remeinder is smaller than 0.005 (if you want 2 digits after the dot) then stop the loop.

[Torsten]

... and if you don't know f (as you do in this case), you usually stop if the absolute value of the term added (here: x^i/factorial(i-1)) is smaller than a specified number.

[Bruno Luong]

(hard to find or easy to find it, depending on your understanding of Taylor)

[Torsten]

Yes, but you have to know that it's f(x) = x*exp(x) that you are approximating. Usually the explicit form of f is unknown.