finding the Value of an infinite Series. 209 
computation of its remaining terms. The advantage 
of this method of proceeding will be manifeft, if we 
apply it to the foregoing example of the feries 
+ &c. in the cafe of 
an arch of 45 0 . 
Compute therefore the firfl: twelve terms of this feries 
in the common way. Thefe terms will be as follows : 
t 
= 
r 
t 3 
r 3 
_ r 
3 rr 
3 rr 
~X 
t 5 
r 5 
r 
5 r4 
5 r4 
~*7 
t 7 
r 7 
r 
Jr 6 
7 r * 
~ 7 
i 9 
r 9 
__ r 
9 r* 
9 r 8 
~T 
l" 
r 11 
- r 
nr 10 
iir l ° 
ri 
JIL* 
r 13 
r 
13 ^ 
t' s 
r IS 
_ r 
i5 r ‘ 4 
15 r 14 
~*5 
t 17 
r 17 
__ r 
17 r 16 
i?r i6 
~ 17 
t ' 9 
r 19 
_ r 
jgr 15 
19 r 18 
19 
* ai 
r 21 
r 
r x. . 090 , 909 , 090 , 909 ; 
2,1 r 
^3 
2,1 r* 
~-~rx . 047 , 619 , 047 , 619 ; 
^“■ 23 r“ = r 3 - n . 043 , 478 , 260 , 869 , 
Vol. LXVII. 
E e 
X.OOO, 
