44 
Mr. Morgan on Survivorjhips. 
o' -V ’ : ± + &c. - | X 
abcr J v 
a! me , a" na . a n 'oe 
+ 
abcr abcr 7 ' abcr z 
+ 
a 
m r 
a>,rf + &C - ~ 
S a dn a a 
— X — — + 
2 r aocr 
!/ 
— ^+ a "yf'fp + see. + s ~x^+ , , 
abcr ate ? i 'l aocr aucr 
a" . em 
i T 
a 
/// 
.fn 
aba 
-+ 
a'"' ■ go 
abcr 4 
n S a' em , a + a" . fn a' + a" + a 
+ &C+ — X — + r -j— + 
/// 
g° 
2 r 
abcr 
abcr z 
abcr 3 
*4" &C» 
_//// 
* • gp 
S a'md a" en a . fo 
^ ^^'abcr J ^abc? z ~ r abcr 3 abcr 4 
+ &C. 
S a' a!' .fo 
x + + 
2r 
abcr' 
a' + a" + a • gP 
abcr ^ 
-f* &C» 
In order to fum up- the firflr and fecond of thefe feries let j3 
reprefeat the number of perfons living at the age of F, a 
perfon one year younger than B, and k the number of perfons 
living at the age of K, a perfon one year younger than C. 
Let FK, BC, AFK, and ABC, reprefent the value of an 
annuity on the two and three joint lives of F and K, of B and 
C, of A, F and K, and of A, B and C refpedtively ; then 
r - . S a' be a"d?n a"'cn c u S . £ . x 
will the feries * * ^ + ffffffz +■ + &c * be Z— E7 x 
6 . 
be 
$*r 
a — a' .be dm 
a@nr 
a — a 
a 
,( .dm 
a@*r J 
a' dm en 
"a + zr~3 
a— a - a -—a . en 
a! 4* a . en 
a@xr$ 
, &c. 
S.jS * FK— AFK / 
IT X ~ 
a$Kt 
(- 
/2x r i 
afiitr 
S a' dm . a' a" den n 
X — + , &C. 
br abcr 
abcr 
S dm 
br X for 
.// 
a — a'.dm^ en a — a'—a' .en 
abcr bcr z abcr z ’ 
See. - ) - 6r 
X 
BC — ABC* The fum, therefore, of the two firft feries, or of 
s 
6 
a be a 
x -t“T 
dm 
abcr 
abcr 2 
n S tfV/W , a'.+f'.eH 
+ &c *+r. x ^+-^- 
+ &c. is — x 
. FK— AFK S 
be 
-I- - x BC — ABC. Again, letP reprefent a life one 
y 
year older than B, and let BK, PC, ABK, and APC, repre- 
fent the values of annuities on the two and three joint lives of 
B and 
