[ 4° ] 



IV. Theorem, i. When wis any even number The fine 



n — I n— I " 3 n— 3 _. 



of n a = + 2 J4I 2. « — 2 X + &c. : ^1 — s' to be con- 

 tinued by diminifhing the index of j by 2 till it becomes 

 unity. The upper figns take place when n is of the form 2/ 

 (p being odd) and the lower when it is of the form 4/ Cp being 

 any number). 



u — I 



The general term is + 



« li + I . « — u + 2 - to — — terms 



u — I 



I. 2. 3 - 



•^ 2 



X 2 . X v^ I-.' : + when "-/ is odd I ^^ „ ^^^^^ ^^^^ ^^ 



ti+i. \ (P being odd.) 



— when —IS even J 



+ when — -— IS even | 



{►and n of the form 4/ f/ being any number) 



jp — when • is odd j 



2. When n is any odd number, the fine of « a = + 



«i — 1 n n — 3 n — 2 



2 J + « 2 J + &c. to be continued by diminifhing the 

 index of j by 2 till it becomes unity. The upper figns take 

 place when n is of the form 4/ + i, and the under when of the 

 form 4/ + 3- 



The 



