* Unique property of the inverse of the golden ratio
Added a description of how the golden ratio minus 1 is equal to the inverse of the golden ratio
* Fix typo in OP's PR
Explained what an arithmetic series is, gave the formula for the sum (when finite) and gave two proofs (not just induction) as the 'famous' method by Gauss is too elegant to ignore.
Addressed infinite decimal expansions as well since they are just as important and the title doesn't suggest this article is only about finite decimals