i6^ DE SViMMIS SERIER. NVMEROS 



erit logaritlimis fumendis 



l/?z:/a-/3+/4--/5 4-/<^-/7-V-/S-/p+ etc. 

 feu hoc modo per duplicem feriem 

 |/f-/2+-/4.+/^-i-/8+-/io+/i2+ etc -{-hxVJzi^x-^i) 



-/3-/5— /7-/9-/11 — /13-etc. — /(2X+1) 



fiquidem vtraque feries in infinitum quidem fed 

 tamen parem terminorum numerum continuetur , 

 feu ip{i X vtrinque idem valor tribuatur : quae 

 duplex feries etiam hoc modo exhiberi poteft 



i/?:i;/2-4-/4+/^-f-/8-i- -{-Iqlx-IHx 



-/i— /3-/5— /7— -l{^x—i) 



At ex ipfa noftra ferie fumto x infinito habemus 



/^14-/2-4-/3 4-/4- + lx:=^0-x^ [x-^-Dlx 



vnde fi xl^ feu ad quemlibet terminum / z ad- 

 datur fit 



/2-i-/4+/^+/8 4-.-.+/2^=0-A;+A;/2+(A:+|)/.j: 

 Deinde fi ibi loco x fcribamus 2 x prodit 



/r4-/2+/3+/4+ • • • +hx-0-2 .T+(2^+,i)/2 +(2A^+i)/Ar 



a qua fi illa auferatur relinquitur : 



/i+/3+/5+....+/(2A;-i)z:-A'+(A; + |)/2+j/jtf 



quae fummae fi in illa forma loco vtriusque feriei 

 fubftituantur orietur haec aequatio : 



1/1+^/2 a~0-J+A;/2+(A;+|)/iO 



[ — O-^lIi+iIx 



'YX-'{X-\-\]l2.-'XlX^ 



vnde 



