So a few days ago I posted this question: Investigate the convergence or divergence of the sequence: but unfortunately I didn't receive any answers. After a research, now aware of the existence of difference equations, I have noticed that this question substantially is the same as asking when a $p$-th order linear difference equations with constant coefficients is convergent or not. I know these kind of equations are well studied and a general solution can be found from the characteristic polynomial (this is my limited knowledge on the subject) However the book from which I took the exercise is on series only and does not even mention difference equations. I was wondering if there exist means of attacking this problem, also from the difference equations theory.
2026-04-07 21:12:02.1775596322
On the convergence of a linear difference equation with constant coefficients
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