Useful Formulas

Summation

Equation

$\left(\sum_{i=1}^n c \right) = c + c+ c + \cdots + c$

$cn$

$\left(\sum_{i=1}^n i \right) = 1+2+3+\cdots+n$

$\frac{n(n+1)}{2}$

$\left(\sum_{i=1}^n i^2 \right) = 1 + 4 + 9 + \cdots + n^2$

$\frac{n(n+1)(2n+1)}{6}$

$\left(\sum_{i=0}^n r^i\right) = r^0 + r^1 + r^2 + \cdots + r^n$

$\frac{(r^{n+1}-1)}{r-1}$

Logrithmtic Expressions

Equivalent Expression

$\log \;(a\;*\;b)$

$\log\;(a) + \log\;(b)$

$\log \;(a\;/\;b)$

$\log\;(a) - \log\;(b)$

$\log\;a^n$

$n\;\log\;a$

$\sum_{i=1}^n \log\;i = \log\;1 + \log\;2 + ... + \log\;n = \log (1.2...n)$

$\log\;n!$