Resolution of Algebraical Equations. 145 



To find the value of the error committed when we stop at 

 the w th term of Lagrange's series. 



If we pursue the same method as that used at the beginning 

 of this Section, we get the required error 



I fan + 1 



coefficient of- in ==—— J*{a + x).F(a + x)' +l 

 x n+l.x' + ' 



k" + "- 



+ x T2. X "+°- '-f( a + x) - Fa + xn+ ' 1 ' &c - 



coefficient of- 1 in/(q + ») \( k - F (" + *)Y +1 _J_ 

 x (\ x J ' n + 1 



coefficient of 1 in />+*). jftttt^)"*'.* 



(F(a+x)\ n +* , ) 



the integral commencing from h = o. 



But the part under the sign of integration may be summed, 

 and 



1 A. ^" + a?) 



_ F(a + x) n+l h" 



x" ~ ' x-hF(a + x)' 



therefore the error = coefficient of x"- 1 in 



f(a+x).F(a + x) n +>. f ~ , 



' J h x~/iF(a + x)' 



to be calculated by Definite Integrals, in the next Section. 



Vol. IV. Part I. T 



