52 INVESTIGATION of fome 
Tue fums of thefe feries, however, vary with the variations. 
in the magnitude of 7. For when r=2, 3, 4, &e.. — ae + 
7” Pp 
3 
er does not vanifh, and est becomes refpectively 2 70 ewe 
2,7 oh 2 
P 
4 
b+2) &e. 
Ye 
A® —a™ —— aq” a pe a a fn by Go wo ve Bc. ‘6 r— 
terms .-= 
vm . . 
= when #—1 is a multiple of 2 by an even: number, and-the- 
fam of the: feries is conftant, orinvariable when ™ is-given; let 
the number of the terms oenret 3 great or fmall. This. feries, 
when n is infinitely great, or 7—1 has-to 4 a-ratio greater than . 
any given or affignable ratio, may be confidered as infinite. . 
Rea" 4 BY" + C—c"-4+- ee to. terms. te aie. a 
; Se See 
So peg: Tee ai 2 2. 
A—a +B—é 466 + &c. to terms 
An —a7+ BY — b+ &c; to omen 
terms, X A—a+B.—db 
add +1 
5 cles Oceano rey A" + A—a"+a+B" 4 B—l" 48 
— yrs 
dole. iG x terms Pa "a s ewan fa Ti 
SE ee n—TI 
A®=—A—*?—at B? —B—b"—b + &e. eras 
7"—Pr 
= 0, when 7 = I: 
— 
_— 
It 
