Approximation of e

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This little animation approximates [math]e[/math] (displayed by the horizontal green line) by the sequence (blue line)

[math](1+\frac{1}{n})^n[/math]

and by the series (black line)

[math] \sum_{n=0}^\infty \frac{1}{n!} [/math]


The underlying JavaScript code

 var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 3, 50, 0.5]});
 var line = board.create('line', [[-10, Math.E], [100, Math.E]], {strokeColor: 'green', strokeWidth: 1});
 var seq = board.create('curve', [[0], [1]], {strokeColor: 'blue'});
 
 var seq_add = function() {
    var n = seq.dataX.length,
        val = Math.pow(1 + 1/n, n);
    seq.dataX.push(n);
    seq.dataY.push(val);
 };

 var series = board.create('curve', [[0], [1]], {strokeColor: 'black'});
 
 var series_add = function() {
    var n = series.dataX.length,
        val = series.dataY[n - 1] + 1 / JXG.Math.factorial(n);
    series.dataX.push(n);
    series.dataY.push(val);
 };

 var txt1 = board.create('text', [15, 1.6, function() { return 'n=' + (seq.dataX.length-1) + ': value = ' + seq.dataY[seq.dataY.length - 1]; }], {strokeColor: 'blue'});
 var txt2 = board.create('text', [15, 1.8, function() { return 'n=' + (series.dataX.length-1) + ': value = ' + series.dataY[series.dataY.length - 1]; }], {strokeColor: 'black'});

 var approx = function() {
     seq_add();
     series_add();
     board.update();
     if (seq.dataX.length <= 50) {
         setTimeout(approx, 500);
     }
 }

 approx();