When learning linear difference equations for the first time, many students wonder: Why do we suddenly assume: Is this just guessing? The answer is no. This assumption is made because exponential-type functions behave very nicely under shifting operations. The Original Equation Consider the recurrence relation: Notice that the equation contains shifted terms: To solve such … Continue reading Why Do We Assume Pᵢ = rⁱ While Solving Difference Equations?