Odd numbers take the form , where
is an integer. When
, the last odd number would be 799. So we're adding
By reversing the order of terms, we have
and we can pair up terms in both sums at the same position to write
so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:
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We could also make use of the formulas,
We have