True or False? Homogeneous linear recurrence equations are linear combinations of power functions.

Question

I think the answer is false because although a homogeneous linear recurrence equation is a linear combination, it is composed of constant coefficients. However to solve this equation the solution may include powers... so I'm second guessing myself. Would that make this statement True?

Answer 1

Apparently I was not the only one who was confused if this was True or False? This was the professor's response:

"Nice! #6 is not counted, because question is somewhat ambiguous: Homogeneous linear recurrence relations are not linear combinations of power functions. However the solutions to homogeneous linear recurrence relations are linear combinations of powers of the roots of the characteristic equations."