Latex cheat sheet

\sum_{i=1}^{k+1}i

\frac{k(k+1)}{2} + k + 1

1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots
=
\prod^{\infty}_{j=0}
\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}
\text{, for }
\lvert q \rvert < 1

\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega

\alpha \beta \gamma \delta \epsilon \eta \theta \mu \nu \xi

\int u \frac{dy}{dx} dx = uv - \int \frac{du}{dx}v dx

\mathbf{V}_1 \times \mathbf{V}_2
=
\begin{vmatrix}
    i & j & k \\
    \frac{\partial{X}}{\partial{u}} & \frac{\partial{Y}}{\partial{u}} & 0 \\
    \frac{\partial{X}}{\partial{v}} & \frac{\partial{Y}}{\partial{v}} & 0 \\
\end{vmatrix}

\left(
    \frac{x^2}{y^3}
\right)

f(n) =
\begin{cases}
    \frac{n}{2}, \text{if } n \text{ is even} \\
    3n + 1, \text{if} n \text{is odd}
\end{cases}

\sqrt[n]{1 + x + x + x^2 + x^3 + \ldots}

\begin{pmatrix}
    a_{11} & a_{12} & a_{13}\\
    a_{21} & a_{22} & a_{23}\\
    a_{31} & a_{32} & a_{33}\\
\end{pmatrix}

\begin{bmatrix}
    0      & \cdots & 0      \\
    \vdots & \ddots & \vdots \\
    0      & \cdots & 0      \\
\end{bmatrix}