Convergence of sequence: Difference between revisions

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Line 3: Line 3:
<html>
<html>
<p>
<p>
nth-element of the sequence: <input type="text" id="input" value="1 / n"><br />
nth-element of the sequence: <input type="text" id="input" value="1 / n">,
start at <input type="number" id="startval" value="1">
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="start" onClick="start_approx()">
<input type="button" value="stop" onClick="clear_all()">
<input type="button" value="stop" onClick="clear_all()">
Line 10: Line 10:
<jsxgraph width="500" height="500" box="box">
<jsxgraph width="500" height="500" box="box">
  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 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++;
  };
  };


Line 26: Line 27:
     seq_add();
     seq_add();
     board.update();
     board.update();
     if (seq.dataX.length <= 50) {
     if (n <= 50) {
         TO = setTimeout(approx, 500);
         TO = setTimeout(approx, 500);
     }
     }
Line 35: Line 36:
   var txtraw = document.getElementById('input').value;
   var txtraw = document.getElementById('input').value;
   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();
}
}
Line 40: Line 44:
var clear_all = function() {
var clear_all = function() {
   clearTimeout(TO);
   clearTimeout(TO);
  seq.dataX = [0];
  seq.dataY = [1];
};
};


Line 49: Line 51:
<source lang="javascript">
<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 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++;
  };
  };


Line 65: Line 68:
     seq_add();
     seq_add();
     board.update();
     board.update();
     if (seq.dataX.length <= 50) {
     if (n <= 50) {
         TO = setTimeout(approx, 500);
         TO = setTimeout(approx, 500);
     }
     }
Line 74: Line 77:
   var txtraw = document.getElementById('input').value;
   var txtraw = document.getElementById('input').value;
   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();
}
}
Line 79: Line 85:
var clear_all = function() {
var clear_all = function() {
   clearTimeout(TO);
   clearTimeout(TO);
  seq.dataX = [0];
  seq.dataY = [1];
};
};
</source>
</source>


[[Category:Examples]]
[[Category:Examples]]
[[Category:Calculus]]
[[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);
};