#!/usr/bin/perl

use strict;
use warnings;

my @files = qw(bla1.txt bla2.txt bla3.txt bla4.txt);
my $output = 'blagesamt.txt';

for my $file(@files){
    open(my $fh,'<',$file) or die $!;
    open(my $write_fh,'>>',$output) or die $!;
    while(my $line = <$fh>){
        print $write_fh $line;
    }
    close $write_fh or die $!;
    close $fh;
}