[tex] 1:\left(\dfrac{1}{1} +\dfrac{1}{2} \right) : \left(\dfrac{1}{1} +\dfrac{1}{3} \right) : \ldots : \left(\dfrac{1}{1} +\dfrac{1}{99} \right) \\ = 1: \dfrac{3}{2} :\dfrac{4}{3} :\dfrac{5}{4} : \ldots : \dfrac{100}{99} \\ = 1\cdot \dfrac{2}{3} \cdot \dfrac{3}{4} \cdot \dfrac{4}{5} \cdot \ldots \cdot \dfrac{99}{100} \\ =\dfrac{2}{100} \\ \tt =\dfrac{1}{50} [/tex]
