[Tex/LaTex] How to get big curly braces for an equation with 3 parts

delimitersmath-modepdftex

I am very new to LaTeX. I want to display this:

enter image description here

How should I go about doing this?

Best Answer

Like this:

enter image description here

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{equation}V_i(t) = \max \left\{
\begin{array}{@{}rl@{}}
\text{abandon:} & 0;\\
\text{continue:}&-c(t)+\frac{\sum_{j=1}^N[pV_{i+j/2}(t+2)+(1-p)V_{i-j/2}(t+1)]}{N(1+r)};   \\[1ex]
\text{improve:} &-c(t)-\alpha(t) \\
                &\hfill{}+\frac{\sum_{j=1}^N[pV_{i+1+j/2}(t+2)+(1-p)V_{i+1-j/2}(t+1)]}{N(1+r)}.
\end{array}
\right .
\end{equation}    

\end{document}