Power series v1

What this power series interview question tests

This is a medium-difficulty puzzle that requires you to derive a closed-form expression for a recurrence relation using formal power series techniques. Quant firms use such problems to assess whether candidates can move fluidly between recursive and analytical representations—a skill that appears frequently in pricing, risk modelling, and algorithm design.

The question presents a simple linear recurrence with a constant term, and asks you to solve it not by standard substitution or characteristic-equation methods, but by constructing and manipulating a generating function. This approach tests your comfort with power series as a problem-solving tool: setting up the generating function, translating the recurrence into a functional equation, and extracting the coefficients to recover a_n.

• Generating functions and their formal manipulation
• Linear recurrence relations with constant terms
• Extracting closed forms from functional equations
• Verification and simplification of the result