I did this:

> cat - >1.pl
1
>
> cat - >2.pl
2
>
> cat - >3.pl
3
>
> perl foo.pl ?.pl
1.pl 1
Total value for the 1.pl : 1
2.pl 2
Total value for the 2.pl : 2
3.pl 3
Total value for the 3.pl : 3
Total value accumulated from all the files
is:6>
[download]

Which is the correct total. So either you didn't test it or you didn't specify what you though the errant behavior was. Either will get you down votes.

If you format your code as follows it will be more readable to you and others. You can use ether tabs or spaces, Perl doesn't care.

foreach my $file (@ARGV)
{
    open(FILE, "$file");
    my $sum = 0;
    while (<FILE>)
    {
        chomp();
        $sum+=$_;
        print "$file $_\n";
        $total+=$sum;
    }
    print "Total value for the $file : $sum\n";
    close( FILE );
}
[download]

Also; you already foreach through the files, why not do the copy in the same loop?

Please when you post code place <code> before and </code> after. These html tags put the code into the pretty little boxes you see in other posts. It also keeps the code from fouling up the browsers for those that read your posts. Please read Writeup Formatting Tips again and take it to heart.