User:Gokugohan382/sandbox

Note to others: please don't revert my edits, as I am attempting to try to understand the TeX math type texts

Now it's my sandbox :). User:gokugohan382 08:01, 9 October 2006 (UTC)

$$ \lim_{n \to \infty} estimatedRTT^{ \infty } = a * \sum_{i=1}^{ \infty } (1-a)^i * sampleRTT_i + 0$$

$$ a * \sum_{i=1}^{n} (1-a)^i * sampleRTT_i + (1-a)^n * sampleRTT_n $$

$$ \frac{2.00033mg As}{1L} * \frac{1L}{1000mL} * \frac{9.9mL}{0.5005g} * \frac{1000g}{1kg} = 39.56697mg As/kg = 39.56697ppm $$

$$ \frac{1.10435mg Fe}{1L} * \frac{1L}{1000mL} * \frac{9.9mL}{0.5005g} * \frac{1000g}{1kg} = 21.84429mg Fe/kg = 21.84429ppm $$

$$ \sum_{i=1}^k x_k = 3 * 4^{k-1} * \frac{\sqrt{3}}{4} * \left ( \frac{1}{3} \right )^{2k}$$

$$ \sum_{i=1}^{k+1} x_{k+1} = 3 * 4^{k} * \frac{\sqrt{3}}{4} * \left ( \frac{1}{3} \right )^{2k+2}$$

$$ \sum_{i=1}^n A_3 = 3 * 4^{2} * \frac{\sqrt{3}}{4} * \left ( \frac{1}{3} \right )^{6}$$

$$ \sum_{i=1}^n A_2 = 3 * 4^{1} * \frac{\sqrt{3}}{4} * \left ( \frac{1}{3} \right )^{4}$$

$$ \sum_{i=1}^n A_1 = 3 * 4^{0} * \frac{\sqrt{3}}{4} * \left ( \frac{1}{3} \right )^{2}$$

$$\ \frac{\sqrt{3}}{4} * \left ( 1 + \frac{1}{3} + \frac{4}{27} + \frac{16}{243} \right ) $$

$$\ \frac{\sqrt{3}}{4} * \frac{4}{3} $$

$$\ \frac{\sqrt{3}}{4} * l_n^2 $$

$$\ \frac{\sqrt{3}}{4} * l_n^2 = \frac{\sqrt{3}}{4} $$

$$\ u_1=29000 $$

$$\ r_0=-.000038(10000) + 3.28 $$

$$\ r_0=-.38 + 3.28 $$

$$\ r_0=2.9 $$

$$\ u_1=r_0*u_0 $$

$$\ u_1=2.9*10000 $$

$$\ y = -.000038x + 3.28 $$

$$\ y - 2.9 = -.000038(x - 10000) $$

$$\ m= -.000038 $$

$$\ (10000,2.9), (60000,1) $$

$$\ m= \frac{1-2.9}{60000-10000} $$

$$\ m= \frac{y_2-y_1}{x_2-x_1} $$

$$\ u_1=2*10000 $$

$$\ u_1=2.3*10000 $$

$$\ u_1=2.5*10000 $$

$$\ y = -.00002x + 2.2 $$

$$\ y - 2 = -.00002(x - 10000) $$

$$\ m= -.00002 $$

$$\ (10000,2), (60000,1) $$

$$\ m= \frac{1-2}{60000-10000} $$

$$\ m= \frac{y_2-y_1}{x_2-x_1} $$

$$\ y = -.000026x + 2.56 $$

$$\ y - 2.3 = -.000026(x - 10000) $$

$$\ m= -.000026 $$

$$\ (10000,2.3), (60000,1) $$

$$\ m= \frac{1-2.3}{60000-10000} $$

$$\ m= \frac{y_2-y_1}{x_2-x_1} $$

$$\ y = -.00003x + 2.8 $$

$$\ y - 2.5 = -.00003(x - 10000) $$

$$\ m= -.00003 $$

$$\ (10000,2.5), (60000,1) $$

$$\ m= \frac{1-2.5}{60000-10000} $$

$$\ m= \frac{y_2-y_1}{x_2-x_1} $$

$$\ u_2=21750 $$

$$\ r_1=-.00001(15000) + 1.6 $$

$$\ r_1=-.15 + 1.6 $$

$$\ r_1=1.45 $$

$$\ u_2=r_1*u_1 $$

$$\ u_2=1.45*15000 $$

$$\ u_{n+1}=r*u_n $$

$$\ u_1=15000 $$

$$\ r_0=-.00001(10000) + 1.6 $$

$$\ r_0=-.1 + 1.6 $$

$$\ r_0=1.5 $$

$$\ u_1=r_0*u_0 $$

$$\ u_1=1.5*10000 $$

$$\ u_{n+1}=r*u_n $$

$$\ y = -.00001x + 1.6 $$

$$\ y - 1.5 = -.00001(x - 10000) $$

$$\ m= -.00001 $$

$$\ (10000,1.5), (60000,1) $$

$$\ m= \frac{1-1.5}{60000-10000} $$

$$\ m= \frac{y_2-y_1}{x_2-x_1} $$

$$\ f_{normal} = \frac{m_{block}}{9.8 ms^{-1}} $$

$$\ f_{max} $$

$$\ \mu_s $$

$$\ f_{max}=\mu_s N $$

$$\ g=\frac{2d}{t^2} $$

$$\ d=\frac{1}{2}gt^2 $$

$$\  t =\ \sqrt {2d/g} $$

$$\ h= 6.626*10^{-34} \frac{j}{s} $$

$$\ E = hv $$

$$\ v=f\lambda$$

$$\ c=f\lambda$$

$$ \sum_{x=1}^4 x^3 = 1^3 + 2^3 + 3^3 + 4^3 $$

$$ \sum_{x=1}^n x^k = 1^k + 2^k + 3^k +\cdots+ n^k $$

$$\ S_n =\left ( \left ( n \right ) \left ( n+1 \right ) \bullet \bullet \bullet \left ( n + \left ( k-1 \right ) \right ) \right ) \bullet \left ( 1+ \left ( \begin{matrix} \frac{1}{k+1} \end{matrix} \right ) \left ( n-1 \right ) \right )$$

$$\ S_n = \left ( \left ( n \right ) \left ( n+1 \right ) \right ) \bullet \left ( 1+ \left ( \begin{matrix} \frac{1}{k+1} \end{matrix} \right ) \left ( n-1 \right ) \right )$$

$$\ S_n = \left ( n \right ) \bullet \left ( 1+ \left ( \begin{matrix} \frac{1}{k+1} \end{matrix} \right ) \left ( n-1 \right ) \right )$$

$$\ \left ( n \right )$$

$$\ \left ( n \right ) \bullet \bullet \bullet \left ( n+k \right ) $$

$$\ \left ( n \right ) \left ( n+1 \right ) \bullet \bullet \bullet \left ( n+k \right ) $$

$$\ \left ( n \right ) \left ( n+1 \right ) \left ( n+2 \right ) \bullet \bullet \bullet \left ( n + \left ( k-1 \right ) \right )$$

$$\ S_n $$

$$\ S_n=1^k + 2^k + 3^k + 4^k + \bullet \bullet \bullet + n^k $$

$$\ U_1= 24 $$

$$\ U_2= 24 + 120 $$

$$\ U_3= 24 + 120 + 360 $$

$$\ U_4= 24 + 120 + 360 + 840 $$

$$\ U_5= 24 + 120 + 360 + 840 + 1680 $$

$$\ U_6= 24 + 120 + 360 + 840 + 1680 + 3024$$

$$\ U_7= 24 + 120 + 360 + 840 + 1680 + 3024 + 5040$$

$$\ U_n=1 \bullet 2 \bullet 3 \bullet 4 + 2 \bullet 3 \bullet 4 \bullet 5 + 3 \bullet 4 \bullet 5 \bullet 6 + \bullet \bullet \bullet + n(n+1)(n+2)(n+3)$$

$$\ 1^4 + 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 7^4 + 8^4 + 9^4 + 10^4$$

$$\ 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 + 10^3$$

$$\ T_1= 6 $$

$$\ T_2= 6 + 24 $$

$$\ T_3= 6 + 24 + 60$$

$$\ T_4= 6 + 24 + 60 + 120 $$

$$\ T_5= 6 + 24 + 60 + 120 + 210 $$

$$\ T_6= 6 + 24 + 60 + 120 + 210 + 336$$

$$\ T_7= 6 + 24 + 60 + 120 + 210 + 336 + 504$$

$$\ 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 + 10^2$$

$$\ 5 \left ( 11 \right )$$

$$\begin{matrix} \frac{1}{2} \end{matrix} 10 \left ( 11 \right )$$

$$\begin{matrix} \frac{1}{2} \end{matrix} 10 \left ( 10+1 \right )$$

$$\begin{matrix} \frac{5}{2} \end{matrix} \left ( 30 \right )$$

$$\begin{matrix} \frac{5}{2} \end{matrix} 5 \left ( 6 \right )$$

$$\begin{matrix} \frac{1}{2} \end{matrix} 5 \left ( 5+1 \right )$$

$$\begin{matrix} \frac{1}{2} \end{matrix} x \left ( x+1 \right )$$

$$\frac{1}{2}x \left ( x+1 \right )$$

$$\ S_n= \begin{matrix} \frac{1}{2} \end{matrix} n \left ( n+1 \right )$$

$$\ S_n=a_1+a_2+a_3+ \bullet \bullet \bullet + a_n $$

$$\ S_1=a_1$$

$$\ S_2=a_1+a_2$$

$$\ S_3=a_1+a_2+a_3$$

$$\ S_4=a_1+a_2+a_3+a_4$$

$$\ S_5=a_1+a_2+a_3+a_4+a_5$$

$$\ S_5=a_1+a_2+a_3+a_4+a_5+a_6$$

$$\ v=f\lambda$$

$$\bullet $$

$$\Lambda f$$

$$\ a_1 = 1 \bullet 2$$

$$\ a_2 = 2 \bullet 3$$

$$\ a_3 = 3 \bullet 4$$

$$\ a_4 = 4 \bullet 5$$

$$\ a_5 = 5 \bullet 6$$

$$\ a_n = n \bullet \left ( n+1 \right)$$

$$\ a_n = a_1 + (n - 1)d$$ $$ \left \lbrace a_n \right \rbrace ^\infty _{n=1} $$

$$\ a_1 = 1_1 + (1 - 1)d$$ $$\ a_1 = 1 + (0)1$$ $$\ a_1 = 1 + 0$$ $$\ a_1 = 1$$

$$\ a_2 = 1_1 + (2 - 1)d$$

$$\ a_3 = 1_1 + (3 - 1)d$$

$$\ a_4 = 1_1 + (4 - 1)d$$

$$\ a_5 = 1_1 + (5 - 1)d$$

$$\ a_6 = 1_1 + (6 - 1)d$$