[ 39 ] , 



.". If « be of the form ^p _(p being odd) the fign is + or — 



Ip V . nj 



according as is even or odd .-. as — is odd or even. If n 



° 1 2 



\p — "^ 

 be of the form \p then it is -f- or — as is even or odd 



and •.■ as ~ is even or odd. 



%. When n is odd and •.• v odd the gen. coefF. becomes of 



, . ^ , n. n — V — 2 - - « — I. K+ I - - 7i-\-v — 2 

 this form + 



I. 2. 3 - - - - 1) 



+ 



2 2 2 2 ^_|. I 



n. n — I . n — 3 _ _ to terms. 



I. 



^ . u n — V 

 The ugn is + or — according as — or is even or odd. 



.'. If n be of the form 4/ + i it is + or — as -^- or ' 



4/ +2 — v^\ . -j-Lr. , -- 



^^-^ IS even or odd or .*. as --L_ is odd or even. It n 



2 2 



be of the form 4/- + 3, it is + or — as "^^ "*" 3 ^^ ^ qj. 4-/'+4 ^ , + i , 



2 



v-\- I 



or .•. as — •- — is even or odd. Whence &c, &c, 

 2 



IV. Theorem..- 



