The author discusses the surprising identity of a sum of a specific form and explores how many similar sums can be evaluated in a closed form. It is revealed that sums of a certain form lead to a rational number when following specific conditions, with an algorithm available for finding the value of the sum. The use of the polylogarithm function Lis(z) is highlighted as a method of evaluation. The author goes on to prove the identity of a specific sum and points out cases where the sum results in an integer. The post also includes information on related mathematical concepts.
https://www.johndcook.com/blog/2024/08/03/polylog/