Add the number dismemberment

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Good afternoon, everyone,

I have an issue that I am not able to solve. I am a beginner in programming and starting with Javascript.

I have an integer, I need to take all the numbers smaller and equal to it and make the sum. Ex: number = 5. The sum of the question would be: 5+4+3+2+1.

I wrote it this way:

function somaNumero(numero) {
    var numero = i;
    var numero = (i * (i - 1))/2;
}
console.log(somaNumero);
javascript
  • 1

    Ever thought of a loop?

  • Marcelinha, the sum of Gauss to determine the sum of all natural up to a certain number is given by function somaNumero(n) {
 return (n * (n + 1)) /2;
}

console.log(somaNumero(5));

  • Read: What a mistake I made asking my question?

  • defined the variable number twice. You did not define the variable i. You did not pass the value in the function call Do like this, this line is negligible var number = i; therefore delete it. Change the i by number and change the sign - by the way + Call the function by passing the value console.log(summeNumber(5)); This solution is in the mathematical approach of my answer

1 answer

2

A number loop passed to the function

function somaNumero(numero) {
  var total = 0;
    for(var i = 1; i <= numero; i++){
      total += i;
    }
    return total;
}

//chama a função passando o numero
console.log(somaNumero(5));

The problem with the above implementation is that as the number increases, so does the number of iterations.

Using a mathematical approach to find the sum of N numbers can completely remove the use of the loop for. Let’s try to solve the above problem with a mathematical approach.

1 + 2 + 3 + 4 + 5 + 6 + …… .. + n

Let’s assume that the sum of the series above is total .

total = 1 + 2 + 3 + 4 + 5

Now let’s reverse the series and add the numbers backwards, which will also give the same total.

total = n + (n-1) + (n-2) + (n-3) + (n-4)

Let’s add up the two totals

total + total = (n + 1) + ((n-1) + 2) + ((n-2) + 3) + ((n-3) + 4) + ((n-4) + 5)



2total = (n+1) + (n+1)+ (n+1)+ (n+1)+ (n+1)

2total = n(n+1)

total = (n(n+1))/2

or (number * (number + 1)) / 2

Upshot

function somaNumero(numero) {
  return (numero * (numero + 1)) / 2 
}

console.log(somaNumero(5));

For those who know what an Arithmetic Progression - PA , just note that the formula of the sum of the n first terms of PA (a1,a2,A3,...,an) is given by

Sn=a1+a2+...+ an=((a1+an) n)/2

Since (1,2,3,4,...,n) is a PA of ratio 1, it follows that the sum of n first terms is given by:

   (1+n)⋅n
  _________
      2

total = ((n+1) n)/2

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