134? MONTMORT. 



a long time to convince himself that there would be neither 

 advantage nor disadvantage for B, but that he had come to this 

 conclusion, and so had Waldegrave, who had worked with him 

 at the problem. It would seem however, that this result is 

 obvious, for B has at every trial an equal chance of winning or 

 losing a crown. 



Montmort proposes on his page 408 a problem to Nicolas 

 Bernoulli, but the game to which it relates is not described. 



231. In the fourth problem given in Art. 229, the advantage 

 of B is expressed by the series 



77 + ^2 + 7^ + pi + • • • '^^^ infinitum. 



This series may be summed by the ordinary methods. 



We shall see that a problem of the same kind as the fourth 

 and fifth of those communicated by Nicolas Bernoulli to Mont- 

 mort, was afterwards discussed by Daniel Bernoulli and others, and 

 that it has become famous under the title of the Petersburg 

 Problem. 



232. Montmort's work on the whole must be considered 

 highly creditable to his acuteness, perseverance, and energy. The 

 courage is to be commended which led him to labour in a field 

 hitherto so little cultivated, and his example served to stimulate 

 his more distinguished successor. De Moivre was certainly far 

 superior in mathematical power to Montmort, and enjoyed the 

 great advantage of a long life, extending to more than twice the 

 duration of that of his predecessor ; on the other hand, the 

 fortunate circumstances of Montmort's position gave him that 

 abundant leisure, which De Moivre in exile and poverty must 

 have found it imj^jossible to secure. 



