User blog comment:QuasarBooster/Fibonacci/Lucas Sequence Extentions?/@comment-2033667-20150730151541/@comment-1605058-20150730205832

I believe that if we have two distinct roots with maximal absolute value, then the root of highest multiplicity will be the limit, and if there is more than one with maximal multiplicity - the limit will not exist. However, in that case we might have that sequence will get back to 0 infinitely often, so sometimes even speaking of ratio of consecutive elements will not make sense.