26 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



1.861 



b 



2/(*) - I AM* - f { /(i) - /() [ + { /'W - /(a) 1 



^^ ^/a 2 I J I2 I J 



1.862 



/" i j_ du x i (f^ i d 5 u x 



J " 2 x 12 dx 720 dx? 30240 d# 5 



SPECL4X FINITE SERIES 



1.871 Arithmetical progressions. If s is the sum, a the first term, d the common 

 difference, I the last term, and n the number of terms, 



s = a + (a + 5) + (a + 26) + . . . .[>+(- i)5] 

 / = a + ( w _ i) 8 



s = -\_2a + (n 1)6] 



1.872 Geometrical progressions. 

 j = a + ap + ap 2 + 



p n - i 



P ~ i 



a 



If 



1.873 Harmonical progressions, a, b, c, d, . . . . form an harmonical progression 

 if the reciprocals, i/a, i/b, i/c, i/d, .... form an arithmetical progression. 



1.874. 



x = n 

 I. 



* = i 



^r = - -\ 1 



* = 





