[ 41^ ■] 



Ir wc put J = — , the fcries may be expreffcd thus; z/x 



J_ T _JL- -j- — I i 1 \- c:c. which may be changed into 



y 3 J' 5 J" 7 J' 



the following; equjvaient one, zp X 1 -— + 



^ 1 y 30J'5 — iSj 



^12_ — r &c. whofe two firft terms are even more 



15757' — 2095;'' 



accurate than the three firft of the preceding — and its three firft 



terms more accurate than five of that feries. 



The fecond and third terms of the above feries being reduced 



to a common denominator, their value is -2Z ^ Upon divid- 



• ^5/ 



m^ the denominator of this fradion by its numerator and taking the 



two firfl terms only of the quote for a new denominator, and unity 

 for a numerator, we get the fradion _-i___ or _-_i^_ ; 



which reduced to an equivalent one whofe denominator is 



Q 27 81 243 o 



1 5 jK% becomes ^__ Sr ^Sy ^^Sf 625/ 



iSy' 

 the terms of the n-umerator decreafing in the ratio of 5 j' : 3, i. e. 



in the ratio of the terms of the numerator of the fradion, which 

 arifes from the union of the fecond and third terms of the feries. 



Then 



