Convergence for Series With Terms Defined by a Recurrence Relation

We investigate whether a series Sigma(infinity)(n = 1) xn with terms defined recursively by the relation x(n+ 1) = f (x(n)), for all n = 1, converges or diverges. For the examples studied, the ratio test is inconclusive. We provide a theorem to decide whether such series are either convergent or divergent under some natural analytic conditions.