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If $$[x]$$ denotes the greatest integer less than or equal to $$x$$ then what is the value of $$\sum_{k=1}^{2014} \left[\frac{k}{1007}\right]$$?
Correct Answer: 1009
For $$1 \le k \le 1006$$ the term is 0. For $$1007 \le k \le 2013$$, which is 1007 values, the term is 1. For $$k = 2014$$ the term is 2. The sum is $$1007 + 2 = 1009$$.
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