Edit in JSFiddle

google.charts.load('current', {packages: ['corechart', 'line']});
google.charts.setOnLoadCallback(drawBackgroundColor);
document.getElementById("series").addEventListener('input', function(e){
		drawBackgroundColor();
});
document.getElementById("min").addEventListener('input', function(e){
		drawBackgroundColor();
});
document.getElementById("max").addEventListener('input', function(e){
		drawBackgroundColor();
});
  
function drawBackgroundColor() {
			var min = parseInt(document.getElementById("min").value);
			var max = parseInt(document.getElementById("max").value);
			data = new google.visualization.DataTable();
      data.addColumn('number', 'm');
      data.addColumn('number', 'Sum of a_n from 1 to m');
      
      var user_expression = document.getElementById("series").value;
      
      var partial_sum = 0;
      
      for (var n = min; n <= max; ++n) {
      	var nth_term = parseFloat(eval(user_expression));
        if (!nth_term || nth_term == Infinity || nth_term == NaN) {
        	nth_term = 0;
        }
      	partial_sum += nth_term;
      	data.addRow([n, partial_sum]);
      }
      
      options = {
        'legend': {'position': 'top'},
        hAxis: {
          title: 'x'
        },
        vAxis: {
          title: 'value'
        },
  		  'width': "100%",
        'height': 600,
        'chartArea': {'width': '80%', 'height': '80%'},
        backgroundColor: '#fff'
      };

      var chart = new 							google.visualization.LineChart(document.getElementById('chart_div'));
      chart.draw(data, options);
      document.getElementById("output").innerHTML = " = " + partial_sum;
}

Series Definition (ex "2*n + 1" or "n * n - 1") <input id="series" size="40" value="4 * pow(-1, n) / (2 * n + 1)"><br/>
Min <input id="min" type="number" size="10" value="0"><br/>
Max <input id="max" type="number" size="10" value="100"><br/>
<div id="output">
</div>
<input type="button" value="Plot">
<div id="chart_div"></div>