[tex]\dfrac{1+2+...+50}{4+8+...+100} = \dfrac{1+2+...+50}{4\cdot(1+2+...+25)} = \dfrac{ \dfrac{50\cdot 51}{2} }{4\cdot \dfrac{25\cdot 26}{2} } = \dfrac{{ \dfrac{50\cdot 51}{2} }}{2\cdot 25\cdot 26} = \\ \\ = \dfrac{50\cdot 51}{2\cdot 2\cdot 25\cdot 26} = \dfrac{50\cdot 51}{2\cdot 50\cdot 26} = \dfrac{51}{2\cdot 26} = \dfrac{51}{52} [/tex]
