FANDOM


$ A-B+C-D+E-F\cdots=\cfrac{A}{1+\cfrac{B}{A-B+\cfrac{AC}{B-C+\cfrac{BD}{C-D+\cfrac{CE}{D-E+\cdots}}}}} $

$ \frac{1}{A}-\frac{1}{B}+\frac{1}{C}-\frac{1}{D}+\frac{1}{E}-\frac{1}{F}\cdots=\cfrac{1}{A+\cfrac{A^2}{B-A+\cfrac{B^2}{C-B+\cfrac{C^2}{D-C+\cfrac{D^2}{E-D+\cdots}}}}} $

$ \begin{align} &\frac{1}{A}-\frac{1}{AB}+\frac{1}{ABC}-\frac{1}{ABCD}+\frac{1}{ABCDE}-\frac{1}{ABCDEF}\cdots \\ =&\cfrac{1}{A+\cfrac{A}{B-1+\cfrac{B}{C-1+\cfrac{C}{D-1+\cfrac{D}{E-1+\cdots}}}}} \end{align} $

$ \begin{align} &A-Bz+Cz^2-Dz^3+Ez^4-Fz^5\cdots \\ =&\cfrac{A}{1+\cfrac{Bz}{A-Bz+\cfrac{ACz}{B-Cz+\cfrac{BDz}{C-Dz+\cfrac{CEz}{D-Ez+\cdots}}}}} \end{align} $

$ \begin{align} &\frac{A}{L}-\frac{By}{Mz}+\frac{Cy^2}{Nz^2}-\frac{Dy^3}{Oz^3}+\frac{Ey^4}{Pz^4}\cdots \\ =&\cfrac{A}{L+\cfrac{BL^2y}{AMz-BLy+\cfrac{ACM^2yz}{BNz-CMy+\cfrac{BDN^2yz}{COz-DYy\cdots}}}} \end{align} $

$ \begin{align} &\frac{A}{L}-\frac{ABy}{LMz}+\frac{ABCy^2}{LMNz^2}-\frac{ABCDy^3}{LMNOz^3}\cdots \\ =&\cfrac{Az}{Lz+\cfrac{BLyz}{Mz-By+\cfrac{CMyz}{Nz-Cy+\cfrac{DNyz}{Oz-Dy\cdots}}}} \end{align} $

$ \frac{4}{\pi}=1+\frac{1^2}{2+\frac{3^2}{2+\frac{5^2}{2+\frac{7^2}{2+\cdots}}}} $

$ \frac{4}{\pi}=1+\frac{1^2}{3+\frac{2^2}{5+\frac{3^2}{7+\frac{4^2}{9+\cdots}}}} $

$ \pi=3+\frac{1^2}{6+\frac{3^2}{6+\frac{5^2}{6+\frac{7^2}{6+\cdots}}}} $

$ \frac{\pi}{2}=1+\frac{2}{3+\frac{3\cdot 5}{4+\frac{5\cdot 7}{4+\frac{7\cdot 9}{4+\cdots}}}} $

$ \frac{2}{\pi}=1+\frac{2\cdot 1}{1+\frac{3\cdot 2}{1+\frac{4\cdot 3}{1+\cdots}}} $

$ \frac{\pi}{2}=1-\frac{1}{3-\frac{2\cdot 3}{1-\frac{1\cdot 2}{3-\frac{4\cdot 5}{1-\frac{3\cdot 4}{3-\frac{6\cdot 7}{1-\cdots}}}}}} $

$ \frac{16}{\pi}=5+\frac{1^2}{10+\frac{3^2}{10+\frac{5^2}{10+\frac{7^2}{10+\cdots}}}} $

$ \frac{12}{\pi^2}=1+\frac{1^4}{3+\frac{2^4}{5+\frac{3^4}{7+\frac{4^4}{9+\cdots}}}} $

$ \frac{6}{\pi^2-6}=1+\frac{1^2}{1+\frac{1\cdot 2}{1+\frac{2^2}{1+\frac{2\cdot 3}{1+\frac{3^2}{1+\frac{3\cdot 4}{1+\frac{4^2}{1+\frac{4\cdot 5}{1+\cdots}}}}}}}} $