What is the length of the the midsegment of a trapezoid with bases of length 14 and 22?
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Notice that
2010 ≡ 1 mod 2009
2011 ≡ 2 mod 2009
2012 ≡ 3 mod 2009
...
4017 ≡ 2008 mod 2009
4018 ≡ 0 mod 2009
So really, <em>S</em> is just the sum of the first 2008 positive integers:
where we invoke the formula
and so <em>S</em> ≡ 0 mod 2009.