# Convergence of series

Compute partial sums of the series $\sum_{n=0}^\infty a_n$.

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', [[0], [1]], {strokeColor: 'black'});

var n = series.dataX.length,
val = series.dataY[n - 1] + a_n(n);
series.dataX.push(n);
series.dataY.push(val);
};

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

var a_n;
var start_approx = function() {
var txtraw = docum var board = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox: [-3, 8, 50, -8]});
var series = board.create('curve', [[], []], {strokeColor: 'black'});
var n;

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() {
board.update();
if (series.dataX.length <= 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);
n = parseInt(document.getElementById('startval').value);
approx();
}

var clear_all = function() {
clearTimeout(TO);
series.dataX = [];
series.dataY = [];
n = 0;
};

ent.getElementById('input').value;
a_n = board.jc.snippet(txtraw, true, 'n', true);
approx();
}

var clear_all = function() {
clearTimeout(TO);
series.dataX = [0];
series.dataY = [1];
};