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**We have studied ultracold fermionic few-particle systems consisting of one single impurity atom and an increasing number of majority atoms in another spin state. Starting from one atom in each spin state we observe the convergence of the normalized interaction energy towards a many-body limit by increasing the number of majority atoms one by one.We realize this with a system of fermionic Lithium-6 atoms trapped in a quasi 1D optical dipole potential. In this system we can tune the strength of the repulsive interaction between the impurity and the majority atoms using a confinement induced resonance and probe the system by radio-frequency spectroscopy. This allows us to measure the interaction energy as a function of the number of majority atoms for different values of the interaction strength. We find that the interaction energy for a two particle system with one atom per spin state is very well described by the analytic theory by Busch et al [1]. For an increasing number of majority atoms the interaction energy shows good agreement with numerical few-body calculations. For more than three majority atoms the normalized interaction energy quickly converges to a many-body limit. This limit is close to the prediction from an analytic model describing a single impurity in a bath of fermions which we obtain by adapting the homogeneous solution (McGuire 1965 [4]) to the trapped system.**

[4] J. McGuire, JMP 6, 432 (1965)

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