122 
Dr. price’s 'Theorems 
yearly, is } x 
n — 4 « — i n — i _ . 
' ■+ — ==^4 — . , Sec. continued to 
r r| r 
«xi+- « x i + -J HXI + - 
2 21 1 
2 n terms =|x — ~^-.+ 
r r 
» X I -J-- » x H — 
2 2 
, Sec. continued to 
2 /z terms - {x 
. + 
r r 
«XI+- « X I -f - 
2 2 , 
+ 
3 
T 
n x i + ■ 
, Sec. continued 
to 2 /z terms. But the fumof the firftof thefe two feries, or 
of h 
n n 
X == + — = 
n x i + - h x H — 
2 2 
i, Sec. (=ix— Sec.) is 
r 7 i 
i+- i+- 
2 2 > 
fee p. 1 1 8 . And the fum of the fecond feries is the fame 
with half the fum of the feries — x—^— + 
i +- i + - i + - 
Sec. (2/z). But by the theorem mentioned in the lalt 
12 2 
note, the fum of n terms of the feries - +— +~, Sec. is 
' a a~ a 1 
A~^ x = 5 T* - Therefore, if i +; is fubfti- 
tuted for a> 2 n for #, and h for £ - , the fum of 
rxi + - 
2 
the fecond feries (that is, of \ x x — 
r r 
’ + * * + - 
M 2 
r 
1+ - 
2 
, Sec. 
r 
i + - 
(2 zz) will come out — - x h - - x ■ ; , or 
v / nr r ~ 7 
I + - 
n\ 
r 
l + - 
2 
nr 
X b + b — • 
Therefore, 
