Dyadic-Moment Closure for U_n = Σ_{k=0}^n binom(n,k)^{-1}.

Abstract. We introduce a dyadic-moment closure technique for the inverse binomial sum U_n = Σ_{k=0}^n binom(n,k)^{-1}. Starting from a beta-function integral representation, we derive an exact closed form, a canonical dyadic operator, a closed ordinary generating function, and a complete two-scale asymptotic tower with explicit rational coefficients. The framework extends naturally to parametric deformations U_n(α), yielding new exact identities and certified approximations. This operator-theoretic approach unifies and surpasses standard methods for reciprocal combinatorial sums.