In addition to Marshall's suggestion, I offer up:

• Abusive one-liner:

  my $sum = 0;
  $sum += (-1)**($_+1) * $_ for 1 .. 1000;
  print "$sum\n";
  [download]

• More logical:

  my $sum = 0;
  my $sign = 0;
  for my $i (1 .. 1000) {
      $sum += ($sign ? -1 : 1) * $i;
      $sign = !$sign;
  }
  print $sum;
  [download]

• or:

  my $sum = 0;
  my $sign = 0;
  for my $i (1 .. 1000) {
      $sum += ($sign++ % 2 ? -1 : 1) * $i;
  }
  print $sum;
  [download]

• Smart:

  my $sum = 0.5*(1 + 999)*( (999-1)/2 + 1 ) - 0.5*(2 + 1000)*( (1000-2)/
  +2 + 1 );
  print $sum;
  [download]

Of course, "Smart" can yield round-off issues...