\begin{definition}[Definition:Pentagonal Number/Definition 2]
Pentagonal numbers are defined as
:$\ds P_n = \sum_{i \mathop = 1}^n \paren {3 i - 2} = 1 + 4 + \cdots + \paren {3 \paren {n - 1} - 2} + \paren {3 n - 2}$
for $n = 1, 2, 3, \ldots$
\end{definition}