GENERALIZED NESTED PELL RADICAL SUMS

摘要

This article presents an extended Pell family of polynomial functions gn(x) which includes thewell known Fibonacci, Lucas, Pell, and Pell-Lucas polynomials fn(x), e”(x),pn(x), and qn.(x), respectively. Itinvestigates the convergence of the sequence {Sn(x)} of nested radical sums, where .9(s) =gi(x)+ g2 (x) /g3(x) + I.+ Vg,,(x); it shows that the sequence converges and Um Sn(x) < Ay, where y y(x) = x V x2 + 1, A = A(x) b-y+a a = a(x) = ga(x), and b = b(x)(x).