You just declare \qed at the end of the paragraph, which is essentially what \end{proof} does automatically (with some more bells and whistles you don't need for your situation).
\documentclass{article}
\usepackage{amsthm}
\begin{document}
A paragraph with a QED symbol at the far end. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines.\qed
\end{document}

You can locally change the QED symbol. I suggest a special command for the task you want (a triangle instead of the square).
\documentclass{article}
\usepackage{amsthm}
\newcommand{\triangleqed}{%
\begingroup
\renewcommand{\qedsymbol}{\ensuremath{\triangle}}%
\qed
\endgroup
}
\begin{document}
A paragraph with a QED symbol at the far end. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines.\qed
A paragraph with a QED symbol at the far end. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines.\triangleqed
A paragraph with a QED symbol at the far end. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines. Let's go on with
nonsense words just to get a few lines.\qed
\end{document}
