LaTeX Testing

I've started using $\LaTeX$ for so that I may embed mathematical equations in my blog without resorting to uploading images each time I want an equation up here. This is just a test to see if everything is working properly.

[Note: Those viewing the mobile version of this website will just see lines of meaningless code unless of course you are adept at coding in $\LaTeX.$]

$R_{{\mu}{\nu}} - \frac{1}{2} g_{{\mu}{\nu}} R + g_{{\mu}{\nu}} \Lambda = \frac{8{\pi}G }{c^{4}} T_{{\mu}{\nu}}$

$G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu}$

$e^{ix} = \cos x + i \sin x$

$G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$

$\sum_{n=1}^{N-1} 3^{-n}cos(2n\theta)= \frac{9-3^{-N+2}cos(2N\theta)- 3cos(2\theta)+3^{-N+1}cos[2(N-1)\theta]}{10-6cos(2\theta)}$

$\sum_1^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$

$t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}$

$F_e = \frac{1}{4\pi \epsilon_0} \frac{Q_1 Q_2}{r^2}$

And for
$CH_3COOH_{(aq)} + CH_3CH_2OH_{(aq)} \longrightarrow {CH_3COOCH_2CH_3}_{(aq)} + H_2O_{(l)}$
$K_c = \frac{[CH_3COOCH_2CH_3][H_2O]}{[CH_3COOH][CH_3CH_2OH]}$