Sequences not so far from being arithmetic/geometric.

Let $ (a_n)$ be a sequence determined by its first term, say $ a_0$ and a recurrence formula of the form $ a_{n+1}= f(a_n)$ , where $ f$ is a function in whose domain belong all the ternms of the sequence. In some special cases, we can defined another sequence $ (b_n)$ , ``close to'' $ (a_n)$ and which is either geometric or arithmetic. This will help to decide whether $ (a_n)$ is convergent or not.


Noah Dana-Picard 2007-12-28