[tex]\displaystyle 1+1:1 = \dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+...+\dfrac{1}{2^{\infty}}+1:1 = \\ \\ = \dfrac{3}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{2^{\infty}} = \dfrac{3}{2}+\sum\limits_{k=2}^{\infty}\dfrac{1}{2^k} = \boxed{2}[/tex]
