124 Dr. price's Theorems 
In like manner, a perfon who enjoys an annuity fe- 
cured by land, payable half-yearly, wall have an ex- 
pe&ation of a quarter of a year’s payment more than 
he could be otherwife intitled to ; the value of which is 
Sec. continued to 2 n terms =7- * 
4* 
By the fame reafoning it will appear, that — is the addi- 
tion to be made to the value of an annuity payable quar- 
terly, in order to obtain its value when fecured by land. 
POSTSCRIPT. 
IN the note p. 121. the expreflion 
is given as the fum of n terms of the feries ~ a +^ + + 
Sec. to — n ’ and the expreflion 
n 
a 
X 
2— if “ n »— l a—i > 
> IS 
given as the fum of n terms of the ferie&-+^-M 3 +^.> See. 
The following inveftigation of thefe theorems being- 
very eafy, will not, perhaps, be unacceptable to thofe 
who have ftudied this fubjecSl. 
lili_ I 12 34 - n 
Put A— — +~ + ~ + _ ; , SCC. ~ * B — - + i+i + _ + ’ ScC. -7* 
a a <r a* a" a a a a' a n 
Then ax^i+-+i+i’ Sec. to -7-7? 
a a a* a n ~ l 
and Ax«-i+^,q + i+7&:c. to ^+7= a, 
and 
