# What is the form of the following recursion relation?

by bjnartowt
Tags: form, recursion, relation
 P: 273 Hi all, I have a recursion relation I am trying to solve: ${X_n} = \frac{1}{{1 - {\alpha _0} \cdot {X_{n - 1}}}} \to {X_n} = ?$ What is the "mathematical form" of this recursion-relation? E.g., I know what a homogeneous, linear recursion-relation with constant coefficients looks like, and how to solve it; same with an inhomogeneous recursion relation. But what about this one? (alpha0 = a constant). All I know is that it looks like the closed-form solution to the infinite geometric sum, and I don't know where to go from there. If someone tells me what the mathematical form of this is, I can Google example-solutions that I can work off of, and/or see what a textbook says. bjn