Just make cleaner style and maybe you'll see you error:

my $file_name = 'file';

print "Enter the number in the first batch file:\n";
$f=<STDIN>;

print "Enter the number in the last batch file:\n";
$l=<STDIN>;

for( $f..$l ){
   my $file="$file_name$_.bat";
   system($file) == 0 or die $?;
   sleep(2);
}
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