Brackets around multiple lines

I am trying to put big rounded brackets around some text that contains math formulas:

Jede Teilfolge hat entweder unendliche viele Elemente von $\left( g_{2n}\right)$ oder $\left( g_{2n+1}\right)$.\todo{Add big bracket}
$\left. {\begin{array}{*{20}{c}} {{g_ + } = \lim {a_n} = \lim {g_{2n}} = g}\\ {{g_ + } = \lim {b_n} = \lim {g_{2n}} = g} \end{array}} \right\}{g_ + } = {g_ - } \Rightarrow \lim {g_n} = g = {g_ - } = {g_ + } = \frac{{1 + \sqrt 5 }}{2}$

The result that I am looking for is something along these lines:

( First Line  )
( Second Line )
( Third Line  )

All of the solutions that I have found force me to go into mathmode, clashing with the formulas, or they use tikz in an enumerated list, which I haven't been able to adapt to my situation.

EDIT: Looks like I didn't explain myself too well. Here something I sketched up, hope this explains it better: Of course the brackets should be as tall as the text, and not go over like in my sketch

• Your write-up is a bit confusing: The code you've posted features a single right-hand-side curly brace, yet you also state that you want large "rounded brackets" (same as parentheses?) on both sides of the multiline expression. Please clarify. – Mico Jun 24 '14 at 21:21
• What I am trying to do is wrap the above code inside of parenthesis, so to enclose the whole thing, like you would do with \left( and \right) when in mathmode – ruben1691 Jun 24 '14 at 22:05
• What I do not understand is that you mention using parentheses as in math mode, but all your formulae are maths. So where is the problem, exactly? – Bernard Jun 24 '14 at 22:46

You need the rcases or drcases environment from mathtools:

\documentclass{article}
\usepackage{mathtools}

\begin{document}

Jede Teilfolge hat entweder unendliche viele Elemente von $(g_{2n})$ oder
$(g_{2n+1})$.
$\begin{drcases} g_+ = \lim a_n = \lim g_{2n} = g\\ g_+ = \lim b_n = \lim g_{2n} = g \end{drcases} g_+ = g_- \Rightarrow \lim g_n = g = g_- = g_+ = \frac{1 + \sqrt{5}}{2}$

\end{document}

Note that you're using too many braces; also there's no need to have \left or \right before all delimiters: it's even discouraged, as it affects spacing.

Usually I also recommend to always have braces around subscripts and superscripts, even if they are only one token, but an experienced user knows when to sin against this “rule”. I wouldn't use brackets around the whole construction, but the document is yours; here is how you can do it:

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum} % just for the example
\newsavebox{\tempbox}

\begin{document}
\lipsum*
\sbox{\tempbox}{% \displaystyle \begin{drcases} g_+ = \lim {a_n} = \lim g_{2n} = g\\ g_+ = \lim {b_n} = \lim g_{2n} = g \end{drcases} g_+ = g_- \Rightarrow \lim g_n = g = g_- = g_+ = \frac{1 + \sqrt{5}}{2} % } \begin{pmatrix} \,\parbox[b]{\wd\tempbox}{ Jede Teilfolge hat entweder unendliche viele Elemente von (g_{2n}) oder (g_{2n+1}). }\hfill\, % left alignment \\[\abovedisplayskip] \,\usebox{\tempbox}\, \end{pmatrix}
\lipsum
\end{document} • You are right, I should have used the notation you used in your code, but I haven't really had the time to go back and change all my code to the correct one. The one I posted above was generated ages ago using MathType, since I didn't know a better way! – ruben1691 Jun 25 '14 at 9:10