Parities kinda handy

\(1\) is an \(\color{red}\text{odd}\) number.
\(1 + 2 \) is an \(\color{red}\text{odd}\) number.
\(1 + 2 + 3\) is an \(\color{blue}\text{even}\) number.
\(1 + 2 + 3+ 4\) is an \(\color{blue}\text{even}\) number.
\(1 + 2 + 3+ 4+5\) is an \(\color{red}\text{odd}\) number.
\(\cdots \cdots\)

True or False?

\(1 + 2 + 3 + \cdots + 999 \) is an \(\color{red}\text{odd}\) number.

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