On solving linear recurrences

Abstract

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as n → ∞. This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

Keywords:

• linear recurrence
• first order
• constant coefficients
• nonhomogeneous
• geometric sequence
• iteration
• induction
• limit
• convergence
• Cauchy convergence criterion