The Judsan Identity: A New Identity for the Forward Difference Operator and Its Connection to the Basel Problem

In this paper, I introduce a new identity involving the forward difference operator, which I call the Judsan Identity: Δ_n = 1/(n+1) - 1/n I prove that: ∑ₙ₌₁^∞ Δ_n/n = 1 - π²/6 This identity reveals a hidden telescoping cancellation and provides a new connection between the forward difference operator and Euler's famous Basel problem. The proof uses only elementary techniques: partial fractions and telescoping sums. The identity can also be rearranged to give a new expression for π²: π² = 6 - 6 ∑ₙ₌₁^∞ Δ_n/n This work is part of a broader framework called the ΠΩ-algebra, which generalizes divergent series summation.