string GetWebPageContent(string url)
{
    string result = string.Empty;
    HttpWebRequest request;
    const int bytesToGet = 1000;
    request = WebRequest.Create(url) as HttpWebRequest;

    //get first 1000 bytes
    request.AddRange(0,bytesToGet - 1);

    // the following code is alternative,you may implement the function after your needs
    using (WebResponse response = request.GetResponse())
    {
        using (Stream stream = response.GetResponseStream())
        {
            byte[] buffer = new byte[1024];
            int read = stream.Read(buffer,1000);
            Array.Resize(ref buffer,read);
            return Encoding.ASCII.GetString(buffer);
        }

    }
}

(根据评论中的要求编辑……;))