C 89s ] 
XLI. A Method of finding, by the Help of Sir Ifaac New- 
ton’s binomial theorem, a near Value of the very fiovuly- 
• • XX x^ x^ 
converging infinite Series #+— + — + - + - + &c. when 
x is very nearly equal to 1. By Francis Maferes, Ffq. 
F. R. S. Curfitor Baron of the Exchequer. 
Read July 9, 1778. 
ARTICLE I. 
T F the capital letters a, b, c, d, e, See. be put for the 
numeral co-efficients of the powers of x in the faid 
feries, fo that a ffiall be = i, b = |, c = ~, d=£, e=|, 
and fo on, we ffiall have B=fxA, c = |x b, d = |xc, 
E = 4 x D? 8cc. and the feries x + — + - + - + - + &C will 
\>&=-X + \AXX + \'ZX' ! ' + \CX* + \ V) X s + \ -£. X 6 + X 1 + \CyX iS 
+ 8cc.; in which feries the fractions f ± t {, f , |, tcc. 
which generate the co-efficients of the powers of x in 
the feveral terms after the firft term x, are derived irom 
each other by the continual addition of i to both their 
numerators and their denominators. 
1. This 
