5& INFESfl&A TION of fome 



The fums of thefe feries, however, vary with the variations 

 in the magnitude of r. For when r = 2, 3, 4, &c. — — -f 



■j- does not vaniih, and "7+7 becomes refpedively i~*> -^pp 



-£- &c 



A? — *■ + B" — * + G* — ? + . &c. to ^TZi terms ;= 



4 



— , when n — 1 is a multiple of 2 by an even number, and -the- 



fum of the feries is con ftant or invariable when m is given, let 



the number of the terms ~-l be great or fmall. This feries, 



when n is infinitely great, or a — 1 has to 4 a ratio greater than 

 any given or affignable ratio, may be confidered as infinite. 



A w — a" 1 + B"— - b m + G'"— £"'•+ &c. to ^H terms 



4 ^-»* y» 



A — a + B — b + C — c + &c. to terms 2 2 



4 



A" — *" + B? — *•+ &c, to ^—-i terms, XA^ + B-i 



»— i r'"+ x = 



+ &c. to terms, =——. A CT + A-«'" + « + B w + B-^x^ 



4 4 i -t 



» — I r m + r 



+ &c. to — - — terms = — — zz 1, when rzzi. 

 4 2 ' 



A m — A — cf n — a + B w — B — £'" — £ -f- &c. to ^— terms, 



r w — r . 



=: = o, when r =: 1. 



It 



2 



