Closed-form expressions for channel capacity of repetition-based cooperative networks under adaptive transmission with selection combining are presented under the assumption of independent Rayleigh fading. Specifically, three different adaptive techniques are investigated: 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 SNR, agree very well with the simulated results and definitely show the impact of selection combining on the calculated channel capacity per unit bandwidth