S = \(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{49\cdot50}\)
S = \(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{49}+\dfrac{1}{49}-\dfrac{1}{50}\)
S = \(\dfrac{1}{2}-\dfrac{1}{50}\)
S = \(\dfrac{12}{25}\)