1. A weighting factor learning system comprising: an audio recognition section that recognizes learning audio data and outputs a recognition result; a weighting factor updating section that updates a first weighting factor applied to an acoustic score obtained from an acoustic model and a second weighting factor applied to a language score obtained from a language model which are used in the audio recognition so that a difference between a correct-answer score calculated with the use of a correct-answer text of the learning audio data and a recognition-result score output from the audio recognition section becomes large; a convergence determination section that determines, with the use of the acoustic score after updating the first weighting factor and the language score after updating the second weighting factor, whether to return to the weighting factor updating section to update the first weighting factor and the second weighting factor again; and a weighting factor convergence determination section that determines, with the use of the acoustic score after updating the first weighting factor and the language score after updating the second weighting factor, whether to return to the audio recognition section to recognize the learning audio data and to output the recognition result using the audio recognition section, update the first weighting factor and the second weighting factor using the weighting factor updating section, and determine whether to return to the weighting factor updating section using the convergence determination section to update the first weighting factor and the second weighting factor again.