Power series - pointwise

Approximate the value of

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

for various values of [math]\displaystyle{ x }[/math]. Drag the point 'x', the blue point shows the value of the above series.

nth-coefficient: , start summation at n =

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, s, m = 50;
  var txtraw = document.getElementById('input').value;
  var a_n = board.jc.snippet(txtraw, true, 'x, n', true);
  var n_0 = parseInt(document.getElementById('startval').value);

  x = p.X();
  for (n = n_0, s = 0; n < m; n++) {
    s += a_n(x, n);
  }
  q.moveTo([x, s], 0);
});