ALGEBRA 27 



1.875 In general, 





S- &+ 7 



*= I 



$1, $2, ^s, are Bernoulli's numbers (6.902), f^j are the binomial 



coefficients (1.61) ; the series ends with the term in n if k is even, and with the 

 term in n 2 if k is odd. 



1.876 



.... 

 1234 n 2n n(n + i) 



n(n + i) (n + 2) 

 7 = Euler's constant = 0.5772156649 . . . 



12 



I 



12 



= 

 2O 



1.877 



= T I ^(I-X) (2 - X) 



VQ 



a ~\~ o I O T ~l o 



2 2 3 2 " w 2 6 + i (w + i) (n + 2) 



(n +i)(+ 2) ( + 3) 



(jfe-i)! 

 &A= "T" 



1.878 



(n + i) (n + 2) 



(w + i)(+ 2) ( + 3) 



