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$a^2 + b^2 = c^2$

$$\oint_V f(s) \,ds$$

Sum $\displaystyle \sum_{n=1}^{\infty} 2^{-n} = 1$ inside text

Limit $\lim_{x\to\infty} f(x)$ inside text

Integral $\int_{a}^{b} x^2 dx$ inside text.

The same integral on display: $$\int_{a}^{b} x^2 \,dx$$ and multiple integrals: $$\begin{gather*} \iint_V \mu(u,v) \,du\,dv \\ \iiint_V \mu(u,v,w) \,du\,dv\,dw \\ \iiiint_V \mu(t,u,v,w) \,dt\,du\,dv\,dw \\ \idotsint_V \mu(u_1,\dots,u_k) \,du_1 \dots du_k \\ \oint_V f(s) \,ds \end{gather*}$$

Sum $\sum_{n=1}^{\infty} 2^{-n} = 1$ inside text.

The same sum on display: $$\sum_{n=1}^{\infty} 2^{-n} = 1$$

Product $\prod_{i=a}^{b} f(i)$ inside text.

The same product on display: $$\prod_{i=a}^{b} f(i)$$

Limit $\lim_{x\to\infty} f(x)$ inside text.

The same limit on display: $$\lim_{x\to\infty} f(x)$$

$$\begin{equation} Z=min E \int_{0}^{\infty} exp(-\rho t)\{ \alpha^2[r(t)-x(t)]^2+[\lambda ^ {-1}\frac{d{x(t)}}{d{t}}]^2 \} d{t} \end{equation}$$

Einstein filed equation:

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