Power series - pointwise

Approximate the value of

[math] \sum_{n=0}^\infty a_n\cdot x^n[/math]

for various values of [math]x[/math] nth-coefficient:

The underlying JavaScript code

var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-8,8,8,-8], axis:true, showClearTraces: true});

var p = board.create('glider', [0, 0, board.defaultAxes.x] , {name: 'x'});
var q = board.create('point', [0, 1], {name: '', color: 'blue', trace: true, fixed: true});

p.on('up', function(evt) {

  var x, n, m = 50;
  var txtraw = document.getElementById('input').value;
  var a_n = board.jc.snippet(txtraw, true, 'n', true);

  var s = 0;
  x = p.X();
  for (n = 0; n < m; n++) {
    s += a_n(n) * Math.pow(x, n);
  }
  q.moveTo([x, s], 0);
});