Suppose the user types the value 40391, so I need to incrementally add all values from 1 to 40390, which results in the value 815696245.
Today I do this with a simple for but I realized that the performance is not the best ... Is there any way to make it more performance?
Yes, just use a formula.
resultado = n(n+1)/2
See working:
var num = 40391;
var res = (num * (num - 1))/2; /* adaptado o "-1" para o enunciado da pergunta */
/* que diz que input 40391 resulta em 815696245 */
document.write(res);
Out of curiosity, this sequence generates what we call the "triangular number":
FurtherReading:
link