User:Arichnad/Tmp

= Tania Head = Stub moved (copy+paste) to Tania Head.

= Table =

= Math Sandbox = $$\begin{align} {\pi\over2} &= \sum^\infty_{k=0} {k!\over(2k+1)!!} \\ &= 1 + {1\over3} + {1\cdot2\over3\cdot5} + {1\cdot2\cdot3\over3\cdot5\cdot7} + {1\cdot2\cdot3\cdot4\over3\cdot5\cdot7\cdot9}+\cdots \\ &= 1 + {1\over3}\left(1+{2\over5}\left(1+{3\over7}\left(1+{4\over9}(1+\cdots)\right)\right)\right) \\ &= (1; 1, 1, 1, 1, \cdots)_{({1\over3}, {2\over5}, {3\over7}, {4\over9}, \cdots)} \end{align}$$

$$\begin{align} \pi &= (2; 2, 2, 2, 2, \cdots)_{({1\over3}, {2\over5}, {3\over7}, {4\over9}, \cdots)} \end{align}$$

$$\sum_{k=1}^\infty r^k=\frac{r}{1-r}$$

$$0.999... = 9 \times \sum_{k=1}^\infty .1^k=9 \times \frac{.1}{1-.1} = 1$$

= More Sandbox = ~a (user • talk • contribs) 03:58, 27 June 2008 (UTC)