User:Luosiji/Sandbox


 * $$20x^2+2y^2-5=0\!$$
 * $$36x^2+68xy+36y^2-136x-144y+139=0\!$$
 * $$y-\frac{|x|}{12}=-\frac{4}{5}\sqrt[3]{\left(\left|x\right|+\frac{y}{12}-\frac{9}{4}\right)^2}+2\!$$
 * $$y-\frac{|x|}{6}=\frac{1}{2}\sqrt[3]{\left(\left|\left|x\right|+\frac{y}{6}-\frac{9}{4}\right|-1\right)^2}-\frac{6}{5}\!$$
 * $$\sqrt[3]{x^2}\pm\sqrt{9-x^2}\!$$
 * $$\sum_{i=0}^{n} \sum_{j=1}^{m} {m \choose j} {i}^{m-j} = {\left(n+1\right)}^{m} $$
 * $$\sum_{i=0}^{n} {\left(i+1\right)}^{m}-{i}^{m} = {\left(n+1\right)}^{m} $$
 * $$E[T] \le \lfloor \log_n m \rfloor + 1 + \frac{m-1}{m} \frac{n}{n-1}.$$