Is this an efficient way to compute the value of Pi, where the limit of j \$\propto\$ accuracy?PI = 0;for (var j = 1; j < 100; j+=2) PI += (4/j)*((j+1)%4?1:-1);The formula I used to write this is:$$\pi \equiv \frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\cdots$$
Computationally approximating PI
javascript;performance;algorithm
Your code will work eventually, but this series converges very very slowly.  In fact, as you can read on Wolfram's web site:... this sum converges so slowly that 300 terms are not sufficient to calculate pi correctly to two decimal places! Here's a better way to do it which implements this function:$$ \pi = \sum_{k=0}^\infty \frac{4(-1)^k}{2k+1} \bigg(\frac{1}{2^{2k+1}} + \frac{1}{3^{2k+1}}\bigg)$$(function(){  PI=0;   n=-4;  for(k=0;k<100;k++) {    z = 2*k+1;    n *= -1;    PI += n/z*(Math.pow(2, -z) + Math.pow(3, -z));  }  console.log(PI);})();