Let Pk be defined as the probability that a frame requires exactly k transmissions. Now a frame requires k transmissions exactly when the first k-1 attempts fail .... this happens with probability Pk-1and the k th transmission succeeds , this happens with probability 1-p. Thus the total probability is (1-p) k-1 .
Then the mean number of transmissions is found by weighting each possible number of transmissions with the probability of this number being required. So we have
acknowledgements are never lost was included to guarantee that when a frame has been received undamaged it does not have to be sent again(if acknowledgements could be lost, a correctly received frame whose acknowledgement was lost would have to be transmitted again) .