500500
5001
2001
200200
500051
200021

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For any sequence that can be modeled by a polynomial, you can derive a formula for the sum of the values of the polynomial evaluated at the natural numbers.

The sum of all counting numbers up to n is given by $\displaystyle\sum_{k=1}^{n}k = \frac{n(n+1)}{2}$

In this case, $n=1000$ , and $\displaystyle\sum_{k=1}^{1000}k = \frac{1000(1001)}{2} =500(1000)+500=500500$