how to create an xml using xml writer without declaration element

Use XmlWriterSettings.OmitXmlDeclaration.

Don't forget to set XmlWriterSettings.ConformanceLevel to ConformanceLevel.Fragment.

You can subclass XmlTextWriter and override the WriteStartDocument() method to do nothing:

public class XmlFragmentWriter : XmlTextWriter
{
    // Add whichever constructor(s) you need, e.g.:
    public XmlFragmentWriter(Stream stream, Encoding encoding) : base(stream, encoding)
    {
    }

    public override void WriteStartDocument()
    {
       // Do nothing (omit the declaration)
    }
}

Usage:

var stream = new MemoryStream();
var writer = new XmlFragmentWriter(stream, Encoding.UTF8);
// Use the writer ...

Reference: This blog post from Scott Hanselman.

you can use XmlWriter.Create() with:

new XmlWriterSettings { 
    OmitXmlDeclaration = true, 
    ConformanceLevel = ConformanceLevel.Fragment 
}

    public static string FormatXml(string xml)
    {
        if (string.IsNullOrEmpty(xml))
            return string.Empty;

        try
        {
            XmlDocument document = new XmlDocument();
            document.LoadXml(xml);
            using (MemoryStream memoryStream = new MemoryStream())
            using (XmlWriter writer = XmlWriter.Create(
                memoryStream, 
                new XmlWriterSettings { 
                    Encoding = Encoding.Unicode, 
                    OmitXmlDeclaration = true, 
                    ConformanceLevel = ConformanceLevel.Fragment, 
                    Indent = true, 
                    NewLineOnAttributes = false }))
            {
                document.WriteContentTo(writer);
                writer.Flush();
                memoryStream.Flush();
                memoryStream.Position = 0;
                using (StreamReader streamReader = new StreamReader(memoryStream))
                {
                    return streamReader.ReadToEnd();
                }
            }
        }
        catch (XmlException ex)
        {
            return "Unformatted Xml version." + Environment.NewLine + ex.Message;
        }
        catch (Exception ex)
        {
            return "Unformatted Xml version." + Environment.NewLine + ex.Message;
        }
    }