pi-series.js

const express = require("express");
const app = express();

const cache = [0, 3];

const getPi = (series = 0) => {
  if (series === 0) return 3;

  const middle = 4 * series;
  const head = 4 / ((middle - 2) * (middle - 1) * middle);
  const tail = 4 / (middle * (middle + 1) * (middle + 2));
  return head - tail;
};

app.get("/", (_, res) => {
  res.json({
    result: cache[1],
  });

  cache[0] = cache[0] + 1;
  cache[1] = cache[1] + getPi(cache[1]);
});

app.listen(3000);