Mathematics
Formal Power Series and Their Role in Combinatorics
Quick fact
Formal power series are algebraic objects that ignore convergence entirely. In combinatorics, the infinite sum 1 + 2x + 4x² + 8x³ + … can be treated as the formal expression 1/(1-2x), and the coefficient of xⁿ gives the sequence 2ⁿ without any worry about whether the series converges.
Why this is interesting
You’ve probably heard that 1 + 2 + 4 + 8 + … = -1. That seems impossible, yet in combinatorics, such bizarre equations are perfectly legal and incredibly useful. How?