Convergence of sequence: Difference between revisions

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Compute values of
Compute values of the sequence
:<math> (a_n)_{n\in{\mathbb N}}</math>.
<math> (a_n)_{n\in{\mathbb N}}</math>.
<html>
<html>
<p>
<p>
nth-element of the sequence: <input type="text" id="input" value="1 / factorial(n)">
nth-element of the sequence: <input type="text" id="input" value="1 / n">,
<input type="button" value="Start" onClick="start_approx()">
start at n = <input type="number" id="startval" value="1" style="width:2em"><br />
<input type="button" value="start" onClick="start_approx()">
<input type="button" value="stop" onClick="clear_all()">
</html>
</html>
<jsxgraph width="500" height="500" box="box">
<jsxgraph width="500" height="500" box="box">
(function(){
var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 8, 50, -8]});
var seq = board.create('curve', [[], []], {strokeColor: 'blue'});
var n;


var seq_add = function() {
    var val = a_n(n);
    seq.dataX.push(n);
    seq.dataY.push(val);
    n++;
};
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 TO;
var approx = function() {
    seq_add();
    board.update();
    if (n <= 50) {
        TO = setTimeout(approx, 500);
    }
};
var a_n;
var start_approx = function() {
  var txtraw = document.getElementById('input').value;
  a_n = board.jc.snippet(txtraw, true, 'n', true);
  seq.dataX = [];
  seq.dataY = [];
  n = parseInt(document.getElementById('startval').value);
  approx();
}
var clear_all = function() {
  clearTimeout(TO);
};
</jsxgraph>
===The underlying JavaScript code===
<source lang="javascript">
  var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 8, 50, -8]});
  var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 8, 50, -8]});
  var seq = board.create('curve', [[0], [1]], {strokeColor: 'blue'});
  var seq = board.create('curve', [[], []], {strokeColor: 'blue'});
  var a_n;
  var n;
 
  var seq_add = function() {
  var seq_add = function() {
     var n = seq.dataX.length,
     var val = a_n(n);
        val = a_n(n);
     seq.dataX.push(n);
     seq.dataX.push(n);
     seq.dataY.push(val);
     seq.dataY.push(val);
    n++;
  };
  };


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


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


var a_n;
var start_approx = function() {
var start_approx = function() {
   var txtraw = document.getElementById('input').value;
   var txtraw = document.getElementById('input').value;
   var a_n = board.jc.snippet(txtraw, true, 'n', true);
   a_n = board.jc.snippet(txtraw, true, 'n', true);
  seq.dataX = [];
  seq.dataY = [];
  n = parseInt(document.getElementById('startval').value);
   approx();
   approx();
}
}


})();
var clear_all = function() {
</jsxgraph>
  clearTimeout(TO);
};
 
</source>
 
[[Category:Examples]]
[[Category:Calculus]]

Latest revision as of 09:38, 30 January 2019

Compute values of the sequence [math]\displaystyle{ (a_n)_{n\in{\mathbb N}} }[/math].

nth-element of the sequence: , start at n =

The underlying JavaScript code

 var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 8, 50, -8]});
 var seq = board.create('curve', [[], []], {strokeColor: 'blue'});
 var n;

 var seq_add = function() {
    var val = a_n(n);
    seq.dataX.push(n);
    seq.dataY.push(val);
    n++;
 };

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 TO;

var approx = function() {
     seq_add();
     board.update();
     if (n <= 50) {
         TO = setTimeout(approx, 500);
     }
};

var a_n;
var start_approx = function() {
  var txtraw = document.getElementById('input').value;
  a_n = board.jc.snippet(txtraw, true, 'n', true);
  seq.dataX = [];
  seq.dataY = [];
  n = parseInt(document.getElementById('startval').value);
  approx();
}

var clear_all = function() {
  clearTimeout(TO);
};