[tex] \sum\limits_{k=1}^{50} \Big[(2k-1)^2-(2k)^2\Big] = \\ \\ =\sum\limits_{k=1}^{50} (2k-1-2k)(2k-1+2k) = \\ \\ = \sum\limits_{k=1}^{50} (-1)\cdot (4k-1) = -\sum\limits_{k=1}^{50}(4k-1) = \\ \\ = -4\cdot \dfrac{50\cdot 51}{2} +50 = -4\cdot 25\cdot 51 + 50 = -5050[/tex]
