[ 340 '^ 



of applying Prob. i. let x — /, and (A) / — 'T~ 4- a% taking the 

 n — 2 fluxion of this equation by Prob. i. / — a x x. 7t — 2 + 



?". ^ ;/ — 2. n — 3- 71 — 4- \ ." ' n — 2 - - n — 6 



-f- Src. 



ixx • -1 2 A' X -— — : 



3. 2. 1 f 5. 4 - - I 



3 

 fubftituting for the fluxions of x, /, /, &c. and dividing by 



ij 2 - - « we get the general equation 



n n — 2 4 



/ _J ^ V '— — / 



I - - n~ "1.2^1.2- n — 3 « — I . « I - - 4 ^ 



»-4 



X + &G. when - is odd to be continued 



I - - n — 4 n — 1 . ;/ 2 



2 



to terms. When - is even, the lafl: term is - — . j , 



4 2 I. 2' - - « 



n n 

 n — I. ri 



Whence taking n = 4, 6, 8, &c. 



J= ~+ — +, &c. = — + H- + — ^ 



2 1.2.3.4 1.2 1.3-4 I-3-3-5 I-3-3-5-7-S 



. ^~ + &c. 



^ I-3-3-5-7-9-5 



Example 



