164 AN EXAMINATION OF SOME QUESTIONS 



and in a similar manner, we may find that which arises from 

 the fourth is expressed by 



{"-K^^n^' + '-"':'-"' ) } (-1)'. 



The mode of continuation is sufficiently obvious, and by ar- 

 ranging all these profits together, we have 



n { (-1)"} 



{.,,( (-l)"+(-l> )}(-l)c 



&c. &c. 



The part which depends on u is easily determined to be 

 (p — q^ u, where 2^ and q are the number of successful and of 



unsuccessful cases, the remaining part consists of — ^ multi- 

 plied by a function of the quantities a, b, c. Sec. In order to 

 abridge as much as possible, I shall write a instead of ( — 1)", 

 b instead of ( — 1)', and so on; so that ab will represent 



(-l)-X 



