标签： 考研数学二

$1+2+3+$ $\cdots + n =$ $\frac{1}{2} \cdot n \cdot (n + 1)$

$S_{n} = \frac{a_{1} \cdot (1 – q^{n})}{1 – q}$

$a_{n} = a_{1} \cdot q^{n-1}$

$b = \frac{a + c}{2}$

$S_{n} =$ $n \cdot a_{1} + \frac{n \cdot (n – 1)}{2} \cdot d$

$S_{n} = \frac{a_{1} + a_{n}}{2} \cdot n$

$a_{n} =$ $a_{1} + (n – 1) \cdot d$

$\log_{a}^{N} =$ $b \Leftrightarrow $ $a^{b} = N$

$\log_{a}^{a} = 1$

$\log_{a}^{1} = 0$

换底公式：$\log_{a}^{M} = \frac{\log_{b}^{M}}{\log_{b}^{a}}$

$\log_{a}^{\sqrt[n]{M}} = \frac{1}{n} \cdot \log_{a}^{M}$

$\log_{a}^{M^{n}} = n \cdot \log_{a}^{M}$

$\log_{a} \frac{M}{N} = \log_{a}^{M} – \log_{a}^{N}$

$\log_{a}^{(M \cdot N)} = \log_{a}^{M} + \log_{a}^{N}$