Discussion on the box dimension of two sequences after basic operations and the convergence or divergence of the corresponding series

After mapping a sequence to a set of points in the discrete space, properties of the discrete space can be investigated by researching the box dimension of the sequence. In this paper, we mainly analyzed the relationship between the box dimension of two positive sequences after addition, subtraction, or multiplication and the original sequences. Based on the investigation in prior work, we dealt with the convergence or divergence of the corresponding series of the above calculated sequences. Moreover, certain important preliminary research results were obtained.