C# + XML writing

I'm trying a little self study and i'm having a problem with the following. Any code help or if you know a resource that can explain how to properly write the code would be amazing.

Here is the output i'm looking for in my XML file:

<?xml version="1.0" ?>
<Document>
     <Pair>
          <Name>somevalue</Name>
          <Value>somevalue</Value>
     </Pair>
     <Pair>
          <Name>somevalue</Name>
          <Value>somevalue</Value>
     </Pair>
</Document>

Here is my code:

public void saveXML()
            {
                  XmlDocument xmldoc;
                  XmlNode xmlnode;
                  XmlElement xmlelem;
                  XmlElement xmlelem2;
                  XmlText xmltext;

                  xmldoc=new XmlDocument();
                  //let's add the XML declaration section
                  xmlnode=xmldoc.CreateNode(XmlNodeType.XmlDeclaration,"","");
                  xmldoc.AppendChild(xmlnode);
                  
                  //let's add the root element
                  xmlelem=xmldoc.CreateElement("","Document","");
                  xmldoc.AppendChild(xmlelem);

                  for(int i=0; i < 3;i++)
                  {
                        //add a pair
                        xmlelem=xmldoc.CreateElement("","Pair","");         // <<--Recieve error here
                        xmldoc.AppendChild(xmlelem);                             //

                        //let's add another element (child of the Pair)
                        xmlelem = xmldoc.CreateElement("","Name","");
                        xmltext =xmldoc.CreateTextNode( "somevalue");
                        xmlelem.AppendChild(xmltext);
                        xmldoc.ChildNodes.Item(1).AppendChild(xmlelem);

                        xmlelem2 = xmldoc.CreateElement("","Value","");
                        xmltext =xmldoc.CreateTextNode( "somevalue" );
                        xmlelem2.AppendChild(xmltext);
                        xmldoc.ChildNodes.Item(1).AppendChild(xmlelem2);
                  }
                  //save the XML document in a file: C:\namevalue.xml
                  xmldoc.Save("c:\\namevalue.xml");
            }

Thanks for your time!