Lossless steering Order of Magnitude estimation

Question

This is an equation from Rau's book "Quantum theory-an Information Processing Approach". It's leading to "lossless steering" of a particle if you insert an infinite number of filters between the initial state and the last filter and for the last step you have to substitute x for $2^n+1$ (n: number of filters) an then let $n\to\infty$. I am a little bit lost because I don't know to handle the $O(f(x))^x$ expression and arrive at the right hand side for $x\to\infty$. Any suggestions on what to read up on, or hints for a solution? Thanks. $$(1 - O(1/x^2)) ^ x \approx 1 - O(1/x)$$