Survivorjhips, 
i AN *11 ! S d a" a'" « . S a f bc a"md a' r > 
than A;wi41be «= — x - + — + -r + &c.+ — - x — 4- -7- + 
/ a r r~ r 5 'labc r r - 
*57 
ns 
^abc 
0 S a'md d'ne a!"of « , S a'mc , d'nd a'"oe 
-+ &c. + — 7 " x — + — + -y + &C. +r-r x — 4* ~4- — 
^abc r r L i* have r r 2, r s 
n S dbd , d'mjs , d"nf c 
+ &C. + 7 — -x — + __ + — + &c. 
1 6 ai< r r 2 r 3 
S a'c , W , a'"e , „ 
— X — + — + &C. 
lac r r r i 
S dd d'e d"f « S a'b d'm d"n n 
x — + — +~ + &C. - — ■ X — + _ + &c* 
1 2*w r r lab r r r 3 
Sx—+— + a ^+ & c. — G + M-U + E. 
Zab r r 2, r 3 
When the life of A is the oideft of the three lives, the fym- 
bols being changed as in the two preceding problems, the value 
of the reverfion will become = 
s 
, , x — - 4 — 7 - + 4 “ &o. -*■ 
babe r r i 3 
X 4 - 
Zabcr r 
msc' , nt . c' + c 
+ &C. + 
bsc' , mtc" . nuc'" 
babe 
x— 4 
+ Si c» + 
i_ x lE + !!!4±i + &c. 
r r 
3 abc 
+ &c. 
x x ^ + ^ + &,ax^ + ^ + ^ &t + 
aato- r r 1 3 ah r r r 
X 
Zabcr r 
nt.S o«.<- + S' + &Ci + ± x a-s.c^ s-^.c" , 
2 ac 
+ 
. S s—t.c't^u.c^re 
+ &C.+ — x — — + 
aer r r 
& c. 
, the 
firft eight feries may be found = M - E ; and the laft two 
.feries being eafily refolved into x —L + izf + ill? 4. & c . — 
JL x a - s - c - e ' + 1 zl • ^£ ±£ + &c. • — £- x • f -< 
2*c r r a r r 2 
+ &c. are = G — D. Hence the general rule, as in the former 
cafe, becomes = G + M — D + E. 
Vol. LXXXI. M m 
When 
