Summing series using recurrence relations
General Mathematics
2026-01-19 v1
Abstract
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation yields a closed form for the series. This method is used to sum several series and to solve two {\it American Mathematical Monthly} problems.
Cite
@article{arxiv.2601.10777,
title = {Summing series using recurrence relations},
author = {Erik Talvila},
journal= {arXiv preprint arXiv:2601.10777},
year = {2026}
}