First problem which springs to mind: if you press the button twice, it will keep going, adding lines.
Second problem: How many rows in your log file? You only allow for 1000 in your arrays, so if it exceeds that...
But please, look at what you are doing! What do you need the array for? All you do with it is read a line, convert it to a double, and store it. Later, you square the value, store that in another array, and then use that array to sum the values. You do not refer to the arrays ever again!
So why use them? And why invoke? It's a button click event, so it's on the correct thread already!
Why not:
private void button1_Click(object sender, EventArgs e)
{
StreamReader sw = new StreamReader("C:\\Users\\Sony\\Desktop\\logfiles\\transm10.txt");
double sum = 0.0;
do
{
double value = Convert.ToDouble(sw.ReadLine());
sum += value * value;
} while (sw.ReadLine() != null);
sw.Close();
textBox1.Text = sum.ToString();
}