{\displaystyle \sum _{k=0}^{\infty }{\frac {1}{2^{k}}}=1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots =2.}
The number of up-arrows refers to the level of the hyperoperation. Two is the only number x such that the sum of the reciprocals of the natural powers of x equals itself.