Merge Multiple text files in a folder

string[] txtFiles;
txtFiles = Directory.GetFiles(txtFileDestination.Text, "*.txt");
using (StreamWriter writer = new StreamWriter(txtFileDestination.Text + @"\allfiles.txt"))
{
    for (int i = 0; i < txtFiles.Length; i++)
    {
        using (StreamReader reader = File.OpenText(txtFiles[i]))
        {
              writer.Write(reader.ReadToEnd());
        }
    }
}