Dynamically creating text files using shell script

Shell Programming and Scripting
1

Hi All,
I want to create a shell script which dynamically create text files. i am using the following script
$i=1
while [ $i -le 4 ]
do
cat > test_$i.txt
done

but while running the script it was stopping(the cursor not going to next step, i have to enter ctrl+c to make it stop). it is creating only file test_1.txt only. The others are not creating. Can anyone help me out.
> sh myprogramme.sh
Here the control is stopping, i entered ctrl+c to stop
>

2 
#!/bin/sh

i=1
while [ $i -le 4 ]
do
   touch  test_$i.txt
   i=`expr $i + 1`
done
3

Thanks a lot