[tex]\displaystyle \sum\limits_{k=1}^{2007}\Big(1-\dfrac{1}{k}\Big) - 1 -\sum\limits_{k=1}^{2007}\dfrac{k-1}{k} = \\ \\ = \sum\limits_{k=1}^{2007}\Big(1-\dfrac{1}{k}-\dfrac{k-1}{k}\Big) - 1 =\sum\limits_{k=1}^{2007}\Big(1-\dfrac{1}{k}-\dfrac{k}{k}+\dfrac{1}{k}\Big) - 1 = \\ \\ = \sum\limits_{k=1}^{2007}(1-1)-1 = \sum\limits_{k=1}^{2007}(0) - 1 =0 -1 = -1[/tex]
