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Closed-form expressions for ergodic capacity of repetition-based cooperative networks under adaptive transmission with selection combining are derived. According to the changing channel conditions, the source adapts its rate and/or power level while the relays simply amplify and then forward the received signals. Specifically, three different adaptive techniques are investigated under the assumption of independent Rayleigh fading channels: optimal simultaneous power and rate adaptation (OPRA), constant power with optimal rate adaptation (OPA) and channel inversion with fixed rate (TIFR). Among them, for an arbitrary number of relays, TIFR gives the worst channel capacity; OPRA gives the best channel capacity and ORA has a channel capacity quality in between the others. The analysis results, based on the upper and lower bound of the end-to-end signal-to-noise ratio (SNR), agree very well with the simulated results and definitely show the impact of selection combining on the calculated channel capacity per unit bandwidth.