Parities kinda handy

11 is an odd\color{#D61F06}\text{odd} number.
1+21 + 2 is an odd\color{#D61F06}\text{odd} number.
1+2+31 + 2 + 3 is an even\color{#3D99F6}\text{even} number.
1+2+3+41 + 2 + 3+ 4 is an even\color{#3D99F6}\text{even} number.
1+2+3+4+51 + 2 + 3+ 4+5 is an odd\color{#D61F06}\text{odd} number.
\cdots \cdots

True or False?

1+2+3++9991 + 2 + 3 + \cdots + 999 is an odd\color{#D61F06}\text{odd} number.

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