You need only one loop and the use of the modulus operator.
private void btnGo_Click(object sender, EventArgs e)
{
txtresult.Clear(); // TextBox to display results (multiline)
int result = Convert.ToInt32( txtNum.Text ); // textbox to hold value to examine
while (result != 1)
{
if (result % 2 == 0) // it is even
{
result = result / 2;
}
else // it is odd
{
result = result * 3 + 1;
}
// Display Results
txtresult.Text = txtresult.Text + result.ToString() + System.Environment.NewLine;
}
MessageBox.Show("Completed");
}