Introductio in analysin infinitorum

RECURRENTIBUS. 187 CAP. XIII. Quinta vero $\frac{2+z}{9(1+z+zz)}$ comparata cum forma $\frac{A+Bpz}{1-2pz.cos.\Phi + ppzz}$ (218) dat $p=1$, $\Phi = \frac{\varpi}{3} = 60^\circ$; $A = \frac{2}{9}$; & $B = -\frac{1}{9}$, unde oritur terminus generalis $+ \frac{2 \sin.(n+1)\Phi - \sin.n\Phi}{9 \sin.\Phi} (-1)^n z^n = + \frac{4 \sin.(n+1)\frac{\varpi}{3} - 2 \sin.n\frac{\varpi}{3}}{9 \sqrt{3}} z^n$ $(-1)^n z^n = + \frac{4 \sin.(n+1)\frac{\varpi}{3} - 2 \sin.n\frac{\varpi}{3}}{9 \sqrt{3}} (-1)^n z^n$. Col- ligantur hae expressiones omnes in unam summam, ac prodibit Seriei propositae terminus generalis quaesitus $= (\frac{nn}{12} + \frac{n}{2} + \frac{47}{72})z^n \pm \frac{1 [TRUNCATED]