Let (Formula presented.) be a positive real sequence decreasing to 0 such that the series (Formula presented.) is divergent and (Formula presented.). We show that there exists a constant (Formula presented.) such that, for each (Formula presented.), there is a subsequence (Formula presented.) for which (Formula presented.) and (Formula presented.).
Convergence Rates of Subseries
Leonetti P
2019-01-01
Abstract
Let (Formula presented.) be a positive real sequence decreasing to 0 such that the series (Formula presented.) is divergent and (Formula presented.). We show that there exists a constant (Formula presented.) such that, for each (Formula presented.), there is a subsequence (Formula presented.) for which (Formula presented.) and (Formula presented.).
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