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   30     29            1
  ---- + ---- + ... + ---- 
    1      2           30

use strict;
use warnings;
...
  }
  print "n = $n, s = $s\n";
}

n = 1, sum = 0
n = 2, sum = 1
n = 3, sum = 2.5
n = 4, sum = 4.333333333333333

for my $n (1..30) {
  my $s = 0;
...
  }
  print "n = $n, s = $s\n";
}

n = 1, sum = 0
n = 2, sum = 1
n = 3, sum = 5/2
n = 4, sum = 13/3

for my $n (1..30) {
  ...
  push(@nums, $s->numerator);
  push(@denoms, $s->denominator);
}

Can't locate object method "numerator" via package "Math::BigInt" at .
+/frac line ...

use bigrat;
my $x = 1;
print $x->numerator, "\n";