Calculating Pi in JavaScript using Gregory-Leibniz Series

Question

I have to calculate value of Pi using Gregory-Leibniz series:

pi = 4 * ((1/1 - 1/3) + (1/5 - 1/7) + (1/9 - 1/11) + ...)

I want to write a function in JavaScript that would take the number of digits that needs to be displayed as an argument. But I'm not sure if my way of thinking is fine here.

This is what I got so far:

function pi(n) {
  var pi = 0;
  for (i=1; i <= n; i+2) {
    pi = 4 * ((1/i) + (1/(i+2)))
  }
  return pi;
}

How do I write the pi calculation so it calculates values till n?

Answer 1

You could use an increment of 4 and multiply at the end of the function with 4.

n is not the number of digits, but the counter of the value of the series.

function pi(n) {
    var v = 0;
    for (i = 1; i <= n; i += 4) {  // increment by 4
        v +=  1 / i - 1 / (i + 2); // add the value of the series
    }
    return 4 * v;                  // apply the factor at last
}

console.log(pi(1000000000));