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ChallengeSuperchallengeAdvanced Number Theory

Advanced Number Theory · Superchallenge problem

Let f(x)=x1+xf(x)=\dfrac{x}{1+x}, and let fnf^{n} denote the nn-fold composition f∘f∘⋯∘ff\circ f\circ\cdots\circ f. Find 1f2025(1)\dfrac{1}{f^{2025}(1)}.