Introductio in analysin infinitorum

248 DE SERIEBUS EX LIB. I. $(1+\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{5})(1+\frac{1}{7})(1+\frac{1}{11})(1+\frac{1}{13}) \text{&c.},$ unde oritur ista Series $0 = 1 - \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} - \frac{1}{6} - \frac{1}{7} - \frac{1}{8} + \frac{1}{9} - \frac{1}{10} \text{&c.},$ ubi omnes numeri primi, praeter 3 & 5, habent signum —. In genere autem notandum est, quoties omnes numeri primi, exceptis tantum aliquibus, habeant signum —, summam Seriei fore $= 0$. Contra autem quoties omnes numeri primi, exceptis tantum aliquibus, habeant signum +, tum summam Seriei fore infinite magnam. 292. Supra etiam (176.) summam dedimus Seriei $A=1-\frac{1}{2^n}+\frac{1}{4^n}-\frac{1}{5^n}+\frac{1}{7^n}-\frac{1}{8^n}+\frac{1}{10^n}-\ [TRUNCATED]