Introductio in analysin infinitorum

138 DE USU FACTORUM INVENTORUM LIB. I. sunt erutae; ceterae, in quibus Exponentes sunt numeri impares, hic primum occurrunt. Constat ergo omnium quoque istarum Serierum: $1 - \frac{1}{3^{2n+1}} + \frac{1}{5^{2n+1}} - \frac{1}{7^{2n+1}} + \frac{1}{9^{2n+1}} - \&c.$ summas per valorem ipsius $\pi$ assignari posse. 176. Sit nunc $m=1$, $n=3$; erit $k = \text{tang. } \frac{\pi}{6} = \text{tang. } 30^\circ = \frac{1}{\sqrt{3}}$; atque Series §. 172 abibunt in has $\frac{\pi}{6\sqrt{3}} = \frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{10} + \frac{1}{14} - \frac{1}{16} + \&c$ $\frac{\pi\pi}{27} = \frac{1}{2^2} + \frac{1}{4^2} + \frac{1}{8^2} + \frac{1}{10^2} + \frac [TRUNCATED]