318 



divergent series. Following (lie general method we consider tlie 

 determinants 



'■2ii ^=: 





■ c„ 



. Cn+2 



«» C„-|-| r„_|.2 .... C2„_i 



tiien we siiali have 



1 



hn—l — 







• "h— 1 



«/t 



^ïi — 1 ^u ^it-\-l ' 



h—1 



C2,,— 2 



/A ^i- 



These general formulae give no insight in the numerical values 

 of the quantities «t, remembering however that c^ = , it is 



2/,+2 



ohvions tha( they are rational and depending on Ihe Bernonllian 

 numbers only. Moreover the}' are positive, for considering the 

 determinant 



D = 



with arbitrary indices p and rn, we get 



00 GO 00 



D= I j ... \f{u^) /{ii^)...j\n,„_L.i)du^du,...dH,n-i-iu'iu^...Um+i 



{m+\)\JJ J 







, z m 



l«m+l«m+l..-Wm+l 



Hence Z) and in particular every determinant ).k is positive, there- 

 fore the same conclusion holds for ak- By direct calculation we get 

 for the very first quantities aj rather irregular numerical values. 

 We shall find 



a, = 12, a, =g. «, 



252 



79' 



241'. 11 .12 



-,«4 



r'«» 



79 * 60.241 ' 79.52489 

 but these results give no indication about the possible convergence of 



4 



