
388 Dr. WARING on the : a 
Jaft edition of the Meditationes: fe ies 18- rendered: more: | 
correct and general. Aid 
4. Let the fum of a feries required be- exipisitedl iy a sais 
tion of a quantity s, the diftance from the firft’ term of the 
feries, then will the general term be the difference between the: 
two fucceffive fums generally expreffed. 
5. Let the general term: be-an algebraical funtion: of ais 
ft, let it eR cab sO : 
Tit, let 1 be Ste.stetl.2+e+2...2+e+n—1 
and are whole numbers; and m (if the fum of aninfinite. 
{cries of terms. is required) lefs than 2 by two, or more 
Re mm 
then the general term el tel +e ne 
o . Z+ . a 
= 'T, where m.: 
e-ebe+lsztet+2..0. pet nee 
Ste. Ztet+i ft Base ~-Ste+1 .Steta: 
hs 0. ah 
——_ 4 i pe. 
ate. Steti.stet2.zte+3 Shee Stbetl...zstet+a— 1 
whence if 
ebete.atetsestet4..-zbern—ise” “+ Az” 3 Bees tales 
StE+3. S++ 4. Stet 5..- Spepu— 12" 34 Aly” 44 BaP are 
etet4.z2+e+5.--2%+e+2— Tae. tT AUS Be +&c. and fo : 
on; then, if m=2-2, willy=a, 3=b—yA, e=c—3A’— Be 
C=d—-<A’” —JB’—yC, &c.; whence the integral ‘tz infinitum, . 

: ‘ : ; ¥y d 
eye t ite feries, will ——_____- 
or fum of the infinite feries, be Tap) See ee 
£ 
ne ge, i | ri 
2.0 She. Sel «Spet+2 &e. 
The reduction of the general term T into quantities of the” 
before given formulz was publifhed in the Meditationes, printed 
in the year 1774. It was before reduced into formule of the 
fame kind nearly by Mr. Nrcuoxe in the ParisA@s. 
2d, Let:the general term be-T’ = . 
ax? + beh +x? 4 &e, ‘? 
BPE BPEL BLE LI Be port XStfietfpiwspfpmNi Katg-e+ Epi ete plas XK Ke 
where | 
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