The intrinsic connection between the fractal dimension of a real number sequence and convergence or divergence of the series formed by it. (English) Zbl 07922112
Summary: In this paper, we mainly make research on the relationship between convergence or divergence of a class of series and the fractal dimension of the corresponding real number sequence. A new discriminant method named the fractal dimension test to judge convergence or divergence of certain positive series has been proposed. Some examples have also been provided to illustrate this test.
MSC:
| 28Axx | Classical measure theory |
| 37Cxx | Smooth dynamical systems: general theory |
| 37Dxx | Dynamical systems with hyperbolic behavior |
Keywords:
fractal dimension; real number sets; monotone sequences; convergence or divergence of seriesReferences:
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