Convergence of series: Difference between revisions

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(Created page with "Compute partial sums of the series <math> (\sum_{n=0}^\infty a_n</math>. <html> <p> nth-element of the series: <input type="text" id="input" value="1 / n"> <input type="button...")
 
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Line 1: Line 1:
Compute partial sums of the series
Compute partial sums of the series
<math> (\sum_{n=0}^\infty a_n</math>.
<math> \sum_{n=0}^\infty a_n</math>.
<html>
<html>
<p>
<p>
nth-element of the series: <input type="text" id="input" value="1 / n">
nth-element of the series: <input type="text" id="input" value="1 / 2^n">
start summation at n = <input type="number" id="startval" value="0" 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()">
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<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 series = board.create('curve', [[0], [1]], {strokeColor: 'black'});
  var series = board.create('curve', [[], []], {strokeColor: 'black'});
var n;
   
   
  var series_add = function() {
  var series_add = function() {
     var n = series.dataX.length,
     var val = a_n(n);
        val = series.dataY[n - 1] + a_n(n);
    if (series.dataY.length > 0) {
      val += series.dataY[series.dataY.length - 1];
    }
     series.dataX.push(n);
     series.dataX.push(n);
     series.dataY.push(val);
     series.dataY.push(val);
    n++;
  };
  };


Line 32: Line 37:
var a_n;
var a_n;
var start_approx = function() {
var start_approx = function() {
  series.dataX = [];
  series.dataY = [];
   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);
  n = parseInt(document.getElementById('startval').value);
   approx();
   approx();
}
}
Line 39: Line 48:
var clear_all = function() {
var clear_all = function() {
   clearTimeout(TO);
   clearTimeout(TO);
  series.dataX = [0];
  series.dataY = [1];
};
};


Line 47: Line 54:
===The underlying JavaScript code===
===The underlying JavaScript code===
<source lang="javascript">
<source lang="javascript">
var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 8, 50, -8]});
var series = board.create('curve', [[], []], {strokeColor: 'black'});
var n;
var series_add = function() {
    var val = a_n(n);
    if (series.dataY.length > 0) {
      val += series.dataY[series.dataY.length - 1];
    }
    series.dataX.push(n);
    series.dataY.push(val);
    n++;
};
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 TO;
var approx = function() {
    series_add();
    board.update();
    if (series.dataX.length <= 50) {
        TO = setTimeout(approx, 500);
    }
};
var a_n;
var start_approx = function() {
  series.dataX = [];
  series.dataY = [];
  var txtraw = document.getElementById('input').value;
  a_n = board.jc.snippet(txtraw, true, 'n', true);
  n = parseInt(document.getElementById('startval').value);
  approx();
}
var clear_all = function() {
  clearTimeout(TO);
};
</source>
</source>


[[Category:Examples]]
[[Category:Examples]]
[[Category:Calculus]]
[[Category:Calculus]]

Latest revision as of 09:36, 30 January 2019

Compute partial sums of the series [math]\displaystyle{ \sum_{n=0}^\infty a_n }[/math].

nth-element of the series: start summation at n =

The underlying JavaScript code

 var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 8, 50, -8]});
 var series = board.create('curve', [[], []], {strokeColor: 'black'});
 var n;
 
 var series_add = function() {
    var val = a_n(n);
    if (series.dataY.length > 0) {
      val += series.dataY[series.dataY.length - 1];
    }
    series.dataX.push(n);
    series.dataY.push(val);
    n++;
 };

 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 TO;

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

var a_n;
var start_approx = function() {
  series.dataX = [];
  series.dataY = [];

  var txtraw = document.getElementById('input').value;
  a_n = board.jc.snippet(txtraw, true, 'n', true);
  n = parseInt(document.getElementById('startval').value);
  approx();
}

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