Introductio in analysin infinitorum

IN DEFINIEND. SUMMIS SERIER. INFINIT. 131 lem. Quo autem valor harum summarum clarius perspicia- CAP. X. tur, plures hujusmodi Serierum summas commodiori modo expressas hic adjiciam. $1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\&c. = \frac{2^0}{1.2.3} \cdot \frac{1}{1}\pi^2$ $1+\frac{1}{2^4}+\frac{1}{3^4}+\frac{1}{4^4}+\frac{1}{5^4}+\&c. = \frac{2^2}{1.2.3.4.5} \cdot \frac{1}{3}\pi^4$ $1+\frac{1}{2^6}+\frac{1}{3^6}+\frac{1}{4^6}+\frac{1}{5^6}+\&c. = \frac{2^4}{1.2.3....7} \cdot \frac{1}{3}\pi^6$ $1+\frac{1}{2^8}+\frac{1}{3^8}+\frac{1}{4^8}+\frac{1}{5^8}+\&c. = \frac{2^6}{1.2.3....9} \cdot \ [TRUNCATED]