# A necessary and sufficient criterion for the existence of ratio limits of sequences generated by linear recurrences

## TL;DR

This paper establishes a precise criterion to determine when the ratio limits of sequences generated by linear recurrences exist and what their values are, applicable to complex sequences.

## Contribution

It provides a necessary and sufficient condition for the existence and value of ratio limits in sequences from arbitrary linear recurrences.

## Key findings

- Derived a criterion for ratio limit existence
- Applicable to complex sequences from linear recurrences
- Clarified conditions for ratio limit values

## Abstract

We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.