s A = 1 + 1 2 + 1 2 2 + 1 2 3 + . . . fuer Archill , s S = 1 10 + 1 2 2 + 1 2 3 + 1 2 4 + . . . fuer die Schildkroete . {\displaystyle {\begin{aligned}s_{A}&=1+{\frac {1}{2}}+{\frac {1}{2^{2}}}+{\frac {1}{2^{3}}}+...&\quad &{\text{fuer Archill}},\\s_{S}&={\frac {1}{10}}+{\frac {1}{2^{2}}}+{\frac {1}{2^{3}}}+{\frac {1}{2^{4}}}+...&\quad &{\text{fuer die Schildkroete}}.\end{aligned}}}
( 1 ↔ 1 10 ) , ( 1 10 ↔ 1 10 2 ) , ( 1 10 2 ↔ 1 10 3 ) , . . . {\displaystyle \left(1\leftrightarrow {\frac {1}{10}}\right),\left({\frac {1}{10}}\leftrightarrow {\frac {1}{10^{2}}}\right),\left({\frac {1}{10^{2}}}\leftrightarrow {\frac {1}{10^{3}}}\right),...}
