$A_{n}^{m} =$ $\frac{n!}{(n-m)!}$
例如：$A_{5}^{3} =$ $\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}$
$1^{2} + 2^{2} +$ $3^{2} + \cdots + n^{2} =$ $\frac{1}{6} \cdot $ $n \cdot (n + 1) \cdot (2n + 1)$
$1+2+3+$ $\cdots + n =$ $\frac{1}{2} \cdot n \cdot (n + 1)$
$S_{n} = \frac{a_{1} \cdot (1 – q^{n})}{1 – q}$
$a_{n} = a_{1} \cdot q^{n-1}$
$b = \frac{a + c}{2}$
$S_{n} =$ $n \cdot a_{1} + \frac{n \cdot (n – 1)}{2} \cdot d$
$S_{n} = \frac{a_{1} + a_{n}}{2} \cdot n$
$a_{n} =$ $a_{1} + (n – 1) \cdot d$
$\log_{a}^{N} =$ $b \Leftrightarrow $ $a^{b} = N$
$\log_{a}^{a} = 1$
$\log_{a}^{1} = 0$
换底公式：$\log_{a}^{M} = \frac{\log_{b}^{M}}{\log_{b}^{a}}$
$\log_{a}^{\sqrt[n]{M}} = \frac{1}{n} \cdot \log_{a}^{M}$
$\log_{a}^{M^{n}} = n \cdot \log_{a}^{M}$
