[tex]1\dfrac{1}{2}\times 1\dfrac{1}{3}\times 1\dfrac{1}{4}\times ... \times 1\dfrac{1}{100} = \\ \\ = \dfrac{1\cdot 2+1}{2}\times \dfrac{1\cdot 3+1}{3}\times \dfrac{1\cdot 4+1}{4}\times ... \times \dfrac{1\times 100+1}{100} = \\ \\ = \dfrac{\not{3}}{2}\times \dfrac{\not 4}{\not 3}\times \dfrac{\not 5}{\not 4}\times ... \times \dfrac{101}{\not{100}} = \\ \\ =\dfrac{1}{2}\times \dfrac{1}{1}\times \dfrac{1}{1} \times ....\times \dfrac{101}{1} = \\ \\ =\boxed{\dfrac{101}{2}}[/tex]
