c# winform richTextBox 自动显示最后一行

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Text;
using System.Windows.Forms;
namespace WindowsFormsApplication11
{
    public partial class Form1 : Form
    {
        private RichTextBox rtxt = null;
        private TextBox txt = null;
        private Button btn = null;
        public Form1()
        {
            InitializeComponent();
            //RichTextBox
            rtxt = new RichTextBox();
            rtxt.Location = new Point(5, 5);
            rtxt.Width = this.Width-30 ;
            rtxt.ScrollBars = RichTextBoxScrollBars.Vertical;
            this.Controls.Add(rtxt);
            //TextBox
            txt = new TextBox();
            txt.Location=new Point(5,rtxt.Height+5);
            this.Controls.Add(txt);
            //Button
            btn = new Button();
            btn.Text = "发送";
            btn.Location = new Point(txt.Width + 5, rtxt.Height + 5);
            btn.Click += new EventHandler(btn_Click);
            this.Controls.Add(btn);
        }
        /// <summary>
        /// 发送信息
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        void btn_Click(object sender, EventArgs e)
        {
            string message = txt.Text.Trim();
            rtxt.AppendText(message+"\n");
            rtxt.Select(rtxt.Text.Length, 0);
            rtxt.ScrollToCaret();
        }
    }
}