[tex] S = \sum\limits_{x=1}^{50}\Big[g(x) - f(x) \Big] = \sum\limits_{x=1}^{50}\Big[ (2x+3) -(x+2) \Big] = \\ \\ =\sum\limits_{x=1}^{50} (x+1) =\sum\limits_{x=1}^{50} x +\sum\limits_{x=1}^{50} 1 = \\ \\ = \dfrac{50\cdot 51}{2} + 1\cdot 50 = 25\cdot 51 +50 = 1325 [/tex]
