Code which appends data to the first file itself. As my previous answer creates a new file but this solution appends to the first file itself.
static void Main(string[] args)
{
string[] Filename = new string[4] {@"F:\Test\2012_03_05_055030.txt", @"F:\Test\2012_03_05_055035.txt",
@"F:\Test\2012_03_05_055040.txt", @"F:\Test\2012_03_05_055045.txt"};
string text="";
int count = 1;
while(count < Filename.Length)
text += System.IO.File.ReadAllText(Filename[count++]);
System.IO.StreamWriter file = new System.IO.StreamWriter(Filename[0]);
file.Write(text);
file.Close();
count = 1;
while (count < Filename.Length)
File.Delete(Filename[count++]);
}