Mr . Morgan on Survive rJJj Ip s • 
atf d 
ao c 
sb"d b"dt 
+ — ■ + 
‘ 2 ' 
aber' 
X — 
s ; b"e 
6 
be"t 
+ 
ab e 
+ 
ao 
"d 
a 
ber % 
47 
x 
tb”'t 
b" f 
eu 
tb'"f 
ab'" 
b - tu -j- a ^SJ. See. See. Let a, reprefen t 
o 
O 
3 6 6 
the number of perfons living at the age of H, a perfon 
one year younger than A ; let N denote a perfon one year 
older than A, and let the feveral combinations BN, BNC, 
AR, &c. denote, as in the former cafe, the values of annuities 
on the joint lives of B and N, of B, N and C, of A and B, 
&c. ; then by proceeding in the fame manner as in the fore- 
. , n • i r • *b"d tb'"e 0 
going demonitration the leries — + — — r—^ + Scc. may 
° ° 3 aber * 3 aber 1 3 aber 5 J 
be found = — x HK — HBK — 
Z ac 
b'"- 
babo* 1 ~ be 
ab’d sb"e tb'"f 
baber 2 ^ babefi 
AC — ABC 
3 r 
6 ar 
the feries 
b\ 
cs b at 
6 aber ” 6 aber" 
+ AK-ABK^ri-scNC-i-NBCs the feries 
+ &c.-£xHC^HBC 
b'ds b"et b"'fu 0 
" , ■ 4- — 7 — ^ 4- — 7 — \ 4° CCC. ■ 
3^£r 1 %abcr 1 3 aber* 
baber 
and the feries 
d 
x AT - ABT 5 
sd 
ber 
AC -ABC 
^acr 
X 
NT -NTB. Thefe four feries, therefore, fuppofing them all 
to be pofitive quantities are 
* « . ±1K-HBK , AK - ABK 
— x — — — - + ~ 
3 C a 2 
a 
r xHC- HBC + — x AC ~ ABC - A- x NC- NBC - — x 
6 a y °ar $cr 
AT — ABT < s . NT — NBT 
2 ' a 
Vd b"e V”f 
With refped to the ,two remaining 
b'c . b"d 
Vtt. 
^ eneS + # ° * anC * 2 ^^ 2 ^ + 2 ^P + &C ’> 
thefe, it is evident, are to be continued after the deceafe of A 
till the extinction of the joint lives of B and C, and have 
been already proved in the folution of the fecond problem 
in my former Paper, to denote the value of the given fura 
if C ihould furvive B„ Let this value be repre ■ 
fented 
