1²/(1 + 2²/(2 + 3²/(3 + · · · ~ .480175529546832 apparently does not simplify beyond 2 Hypergeometric2F1[2, 2, (5 - 1/√5)/2, 1/2 - 1/(2 √5)]/ ((-1 + 3 √5) Hypergeometric2F1[1, 1, (3 - 1/√5)/2, 1/2 - 1/(2 √5)]) Mathematica has been startling me with valuations of K[quartic,quadratic,...], but not this time. Does anyone know the simple CF 1² + 1/(2² + 1/(3² + · · · = 1.24328847839972? It's probably just a quotient of confluent hypergeometrics. Somewhere in my notebooks may lie a tool Julian built for doing it, but where? --rwg