Table of mathematical constants by q779

Mathematical constant table By q779
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Constant table

$e=2.718281828$

$\pi =3.141592654$

$\ln \pi =1.1447$

$\sqrt{\pi }=1.7725$

Natural logarithm table	$N$	$\ln N$
$\ln 2=0.70$	$2$	$0.6931$
$\ln 3=1.10$	$3$	$1.0986$
$\ln 5=1.61$	$5$	$1.6094$
$\ln 7=1.95$	$7$	$1.9459$
$\ln 11=2.40$	$11$	$2.3979$
$\ln 13=2.56$	$13$	$2.5649$
$\ln 17=2.83$	$17$	$2.8332$
$\ln 19=2.94$	$19$	$2.9444$
$\ln 23=3.14$	$23$	$3.1355$
$\ln 29=3.37$	$29$	$3.3673$
$\ln 31=3.43$	$31$	$3.4340$

$\exp$ surface	$N$	$\exp N$
$\exp 2=7.3891$	$2$	$7.39$
$\exp 3=20.0855$	$3$	$20.09$
$\exp 5=148.4132$	$5$	$148.41$
$\exp 7=1096.6332$	$7$	\tt{} $1096.63$
$\exp 11=59874.1417$	$11$	$59874.14$
$\exp 13=442413.3920$	$13$	$442413.39$

Blackboard bold

$\mathbb{A}\mathbb{B}\mathbb{C}\mathbb{D}\mathbb{E}\mathbb{F}\mathbb{G}\mathbb{H}\mathbb{I}\mathbb{J}\mathbb{K}\mathbb{L}\mathbb{M}\mathbb{N}\mathbb{O}\mathbb{P}\mathbb{Q}\mathbb{R}\mathbb{S}\mathbb{T}\mathbb{U}\mathbb{V}\mathbb{W}\mathbb{X}\mathbb{Y}\mathbb{Z}$

some at sixes and sevens The formula

The prefix sum of the arithmetic sequence ：$S(n)=\frac{n(a_1+a_n)}{2}=n{a}_1+\frac{n(n-1)}{2}d$

Prefix sum of proportional series ：$S(n)=\frac{a_1(1-q^n)}{1-q},q\ne 1$

Some common prefixes and

• $\sum _{i=1}^{n}i=\frac{n(n+1)}{2}$

• $\sum _{i=1}^n{i}^2=\frac{n(n+1)(2n+1)}{6}$

• $\sum _{i=1}^n{i}^3={\left(\frac{n(n+1)}{2}\right)}^2$

Fast square
$$\begin{array}{rl}\sqrt{x}& =a+\frac{x-a^2}{\sqrt{x}+a}\\ \sqrt{x}& \approx a+\frac{x-a^2}{2\times a}\end{array}$$

Positive integer $a$ Satisfy $a^2\le x<(a+1{)}^2$