finding the Value of an infinite Series , 8tc. h i 
* I x xx * 3 X* * 5 * 6 * 7 . . r 
feries — — — + '^r — ^r + Sec. which is of 
the fame form with the feries a - hx + exx - dx* + ex*- 
fx s at 6 - /6x 7 + See. Therefore, if we put a-~,b- 
' = rV> £/ =rr» e ~ TP /= rr> £ = TP * = tp and fo on > and 
compute the differential feries 
bx D* xx D«i* s D ”** 4 D* v * s D**® 
D VI * 7 
^ UA * A 1J" A U A XJ- « ^ ~ ” 0 
* i+*~r+ r iT mv xT ^ 4 i+^ 1 5 it ?? i+3 7 KC * 
thence refulting, the number thereby obtained will be 
the value of the feries +f-J+ &c. 
25 27 29 31 33 35 37 39 
or 
" + ' 
r" t 
: + 
39 f 
25 27 rr 29r* 3xr 6 33^ 3Sr“ 37 r 
computation is as follows : 
Here a is = ^= .040,000,000,000; 
b = ^=.037,037,037,637; 
f =^ = .034,482,758,620; 
d =^=.032,258,064,516; 
f = TT = -° 3 0 J 3 0 3 >° 3 °> 3 o 3 ? 
/ = ^=.028,571,428,571; 
g =^=.027,027,027,027; 
£ = 3V = .025,641,025,641. 
■+ 8cc. This 
E e 2 
Tlie 
