The formatting of your post is fine, but you should choose a better node title. See
How do I compose an effective node title?. This will help you to get a better response.
With regards to speeding up your code, you could try to profile it. See the Tutorials section: Profiling your code.
I would also appreciate any constructive criticism on my code, I am here to learn.
perlcritic is a handy tool for automatically criticizing your code.
for($i = $value; $i <= $range; $i++){
A more Perl-ish way to write this for loop is:
for $i ($value .. $range){
Also
print $fibValue1.' / '.$fibValue2.' = '.$phiApprox;
can be written as (with less typing):
print "$fibValue1/$fibValue2 = $phiApprox";
Update: fixed link.
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